GEOMETRY and MEASUREMENT

Transcription

1 GEOMETRY and MEASUREMENT

2 Table of Contents Let s Stay in Shape!... 1 Line Up!... 2 Get a Good Angle on This One... 3 Measuring Angles...4 Cutting Up... 5 What a Class!... 6 Same As...7 This Works in Any Language!... 8 Mirror Images... 9 Looking in the Mirror It s Customary Metrically Speaking...12 On the Border Using Measures Half the Work...17 Areas of Trapezoids Going Around In Circular Thinking...20 Parts Sectioned Off...21 Diagram Data...22 Block Party Rolling Along...25 Volumes of Prisms...26 Volumes of Cylinders...27 Egyptian or Mexican Design? One Scoop or Two?...29 Using a Model Volumes of Irregular Figures...32 It s a Cover-Up VersaTiles Geometry and Measurement R ISBN Greenview Court Vernon Hills, Illinois hand2mind.com 2009, 1999 by ETA hand2mind. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission of the publisher. Developed and printed in the United States of America

3 Let s Stay in Shape! A line is a straight path of points that extends infinitely in opposite directions. A line segment is a part of a line. It has two endpoints and a definite length. A ray is a straight path of points that starts from one endpoint and extends infinitely in one direction. An angle is formed by the meeting of two rays at a vertex. Match the description with its geometric concept. 1 the horizon 3 the top of a classroom chalkboard, from one end to the other 5 the figure formed by a classroom flagpole and the wall on which it is hanging 7 the shape of the pole holding a classroom flag 9 the thing you roll in a typical board game 11 all the points in space that are exactly the same distance from you at this moment 2 a rubber ball sliced in half 4 the shape of a pane of glass in a window of a classroom 6 a beam from a flashlight pointed at the sky 8 the smallest dot that can be drawn on a piece of paper 10 the shape of a typical box of tissues 12 all the points on the floor of a classroom that are exactly the same distance from you at this moment Angle Sphere Hemisphere Ray Cylinder Rectangular prism Line segment Cube Circle Point Rectangle Line Objective: Identify a line, line segment, ray, angle, 2-dimensional shape, and 3-dimensional shape. 1

4 Line Up! Intersecting lines cross each other or, if extended, will cross each other. Perpendicular lines intersect to form a right angle. Parallel lines are lines in the same plane that do not intersect. Use the diagram at the right. Which line(s) are: 1 parallel to line m? 2 perpendicular to line q? 3 parallel to line o? 4 perpendicular to line s? 5 parallel to line m and perpendicular to line s? 6 intersecting, but not perpendicular to line o? 7 parallel to line n? 8 parallel to line p? 9 perpendicular to line o? 10 parallel to line r? 11 intersecting, but not perpendicular to line m? 12 parallel to line q and perpendicular to line n? Lines m, n, q, r Lines m, n Lines o, p Line n Line p Line s Line o Line r Line q Line m Lines o, p, s None 2 Objective: Identify lines as intersecting, perpendicular, or parallel.

5 Get a Good Angle on This One Choose the correct angle to complete the sentence. 1 is a right angle. 2 is a straight angle. 3 is an acute angle. 4 is an obtuse angle. 5 is an acute angle. 6 is an obtuse angle. 7 is a straight angle. 8 is an obtuse angle. 9 is an acute angle. 10 is not an obtuse angle. 11 is not an acute angle. 12 is not an acute angle. WOY WOZ XOZ VOX ROV SOZ WOY SOX TOQ ROU QOV SOU SOQ ROY SOZ ZOX WOZ MOY MOW MOY QOV SOU ROV WOY WOZ MOY VOX SOX UOZ SOU MOV ROU SOQ UOZ TOW WOY SOU MOW ROV UOZ MOV SOQ QOV WOZ MOY SOZ WOY VOX Objective: Identify an angle as acute, right, obtuse, or straight. 3

6 Measuring Angles Find the measure of the angle. 1 2 M Remember! Use the inner scale of a protractor if an angle opens from the right. Use the outer scale if it opens from the left Objective: Measure an angle using a protractor.

7 Cutting Up Use the diagram to answer the question. m E = 124 m G = 124 What is the measure of the angle? 1 C 2 F 3 I What is the sum of the measures of the angles? 4 H and J 5 M and C 6 E and K 7 P and H 8 G and N 9 What is the difference between the measures of K and D? 10 What is the difference between the measures of P and A? 11 What is the sum of the measures of C, H, I, and N? 12 What is the sum of the measures of H, E, and Q? Objective: Identify the relationships between angles formed when parallel lines are cut by a transversal. 5

8 What a Class! Find the figure that best fits the description. 1 a triangle with no sides congruent and one obtuse angle 2 a triangle with a right angle and two congruent sides 3 a quadrilateral with opposite sides congruent, consecutive sides different lengths, and all right angles 4 a quadrilateral with all sides congruent and no right angles 5 a triangle with no angles equal to or greater than 90 and no congruent sides 6 a quadrilateral with 4 congruent sides and all right angles 7 a quadrilateral with opposite sides parallel and congruent and with consecutive sides different lengths 8 a triangle with a right angle and no congruent sides 9 a quadrilateral with exactly one pair of parallel sides 10 a quadrilateral with no pairs of parallel sides 11 a triangle with all sides congruent 12 a triangle with no angles equal to or greater than 90 and one pair of congruent sides Figure ABC is a right scalene triangle. Figure DEFG is a parallelogram, a rectangle, a rhombus, and a square. 6 Objective: Classify triangles and quadrilaterals.

9 Same As Use the given information for each pair of congruent figures to find the correct answer. ABC DEF AB corresponds to DE. BC corresponds to EF. Trapezoid LMNP Trapezoid QRST MN is parallel to LP. MN corresponds to RS. NP corresponds to ST. 1 Which side corresponds to AC? 2 Which angle corresponds to DFE? 3 Which angle corresponds to FDE? 4 Which side is parallel to RS? 5 Which side corresponds to ML? 6 Which angle corresponds to MNP? 7 Which angle corresponds to PLM? 8 Which angle corresponds to NML? Quadrilateral UVWX Quadrilateral PQRS VUX is a right angle. UV corresponds to PQ. WX corresponds to RS. VW corresponds to QR. 9 Which angle in quadrilateral PQRS is a right angle? 10 Which angle corresponds to VWX? 11 Which angle corresponds to UVW? 12 Which side corresponds to XU? means is congruent to. RST ACB TQR QRS CAB QPS SP SRQ QT DF RQ PQR Objective: Identify a figure as being congruent to a given figure. 7

10 This Works in Any Language! Remember! Apply the translation to each coordinate of the original figure. Find the coordinates of the missing vertex of the translation image. Original Figure Translation Rule Translation Image 1 (2, 5), (7, 5), (7, 10) (+ 2, + 4) (4, 9), (9, 9), 2 (1, 0), (8, 0), (1, 12) (+ 5, + 1) (6, 1), (13, 1), 3 (7, 11), (11, 12), (14, 19) (+ 8, + 3) (15, 14), (19, 15), 4 ( 2, 0), ( 4, 1), ( 6, 5) (+ 7, + 8) (5, 8), (3, 7), 5 ( 3, 5), ( 8, 9), ( 2, 12) (+ 6, + 2) (3, 7), ( 2, 11), 6 (5, 8), (1, 9), (6, 6) (+ 8, 2) (13, 10), (9, 11), 7 (10, 6), (9, 15), (7, 5) ( 4, 6) (6, 12),, (3, 11) 8 ( 12, 8), ( 1, 9), ( 4, 3) ( 4, 8) ( 16, 16),, ( 8, 11) 9 (4, 2), ( 3, 2), (0, 0) (+ 5, 2) (9, 4), (2, 0), 10 ( 6, 1), ( 6, 5), ( 2, 5), ( 2, 1) (+ 4, 1) ( 2, 0), ( 2, 4), (2, 4), 11 (7, 8), (1, 1), (5, 9), (4, 7) ( 3, 5) (4, 13), ( 2, 4), (2, 4), 12 (8, 0), (4, 4), (0, 8) ( 9, + 6) ( 1, 6),, ( 9, 14) (9, 14) (1, 3) ( 5, 10) ( 5, 17) (5, 2) (22, 22) (2, 0) (5, 21) (6, 13) (14, 8) (1, 2) (4, 14) 8 Objective: Identify the translation of a figure in a coordinate plane.

11 Mirror Images Find the missing coordinates of the image after it is reflected over the y-axis. Original Figure Reflection ( 4, 8), ( 5, 10), ( 4, 12) (4, 8), (5, 10), 1 ( 2, 5), ( 2, 9), ( 5, 9), ( 5, 5) (2, 5), (2, 9), (5, 9), 2 ( 2, 5), ( 2, 9), ( 5, 9), ( 5, 5) (2, 5), (2, 9), (5, 9), 3 ( 4, 8), ( 5, 10), ( 4, 12) (4, 8), (5, 10), 4 (4, 8), (4, 12), (5, 10) ( 4, 8), 5, ( 5, 10) (2, 5), (2, 9), (5, 9), (5, 5) ( 2, 5), ( 2, 9), ( 5, 9), 6 Look for a pattern in the numbers. Find the missing coordinates of the image after it is reflected over the x-axis. Original Figure Reflection (3, 8), (4, 12), (9, 5) (3, 8), (4, 12), 7 ( 5, 10), ( 6, 14), ( 3, 14), ( 2, 10) ( 5, 10), ( 6, 14), ( 3, 14), 8 ( 5 10), ( 6, 14), ( 3, 14), ( 2, 10) ( 5, 10), ( 6, 14), ( 3, 14), 9 ( 3, 8), ( 9, 5), ( 4, 12) ( 3, 8), 10, ( 4, 12) ( 3, 8), ( 4, 12), ( 9, 5) ( 3, 8), ( 4, 12), 11 (5, 10), (6, 14), (3, 14), (2, 10) (5, 10), (6, 14), (3, 14), 12 ( 2, 10) (2, 10) ( 9, 5) ( 4, 12) ( 9, 5) (9, 5) (5, 5) ( 5, 5) ( 2, 10) (5, 5) (4, 12) (4, 12) Objective: Identify the reflection of a figure in a coordinate plane. 9

12 Looking in the Mirror A line of symmetry divides a figure into two halves that are mirror images of each other. line of symmetry Find the number of lines of symmetry for the figure Find the figure that matches the description. 7 a figure with 6 lines of symmetry 8 a triangle with no lines of symmetry 9 a plane figure with an infinite number of lines of symmetry 10 a quadrilateral with one line of symmetry 11 a quadrilateral with 2 lines of symmetry 12 a triangle with one line of symmetry Remember! You can test your solutions with a mirror. Rhombus Scalene triangle Isosceles right triangle Circle 3 Isosceles trapezoid Regular hexagon Objective: Identify the line(s) of symmetry for a given figure.

13 It s Customary 1 ft = 12 in. 1 c = 8 fl oz 1 lb = 16 oz 1 yd = 3 ft 1 pt = 2 c = 16 fl oz 1 T = 2,000 lb 1 mi = 5,280 ft 1 qt = 4 c = 32 fl oz 1 mi = 1,760 yd 1 gal = 4 qt Find the equivalent measure. 1 4 ft 2 1 yd 2 ft 3 3 c 4 2 lb 5 oz 5 1 qt 3 c 6 2 yd 1 ft mi 8 2 mi 9 1 gal yd 11 4 qt 2 c in. 2,640 ft 48 in. 56 fl oz 16 c 8 ft 60 in. 37 oz 2,550 ft 24 fl oz 18 c 84 in. 3,520 yd Find the equivalent measure in oz 3 72 oz fl oz 5 40 ft in. 7 2,360 yd 8 6,000 ft fl oz qt ft in. 4 lb 8 oz 6 gal 125 fl oz 5 yd 20 in. 1 mi 720 ft 3 qt 4 fl oz 4 ft 11 in. 28 yd 2 ft 13 yd 1 ft 20 yd 30 in. 2 lb 6 oz 7 gal 3 qt 1 mi 600 yd Objective: Convert units of length, capacity, and weight in the customary system. 11

14 Metrically Speaking 1 cm = 10 mm 1 L = 1,000 ml 1 g = 1,000 mg 1 m = 100 cm = 1,000 mm 1 kg = 1,000 g 1 km = 1,000 m Find the equivalent measure cm 5 35 kg g 2 3,500 ml 6 35,000 mm ml g L 11 3,500 g mm km cm m 3,500 m L 0.35 m 35,000 g 3.5 kg 3.5 L 35 m 3.5 m 350 ml kg 0.35 kg Find the equivalent measure kg L 9 83,500 cm m ml kg cm 7 8,350 cm kg kg 8 10,500 ml L 7,500 g 75 g 10.5 L 105 ml km 83.5 mm 83.5 m 750 g L 835 cm 1,050 ml 75,000 g 12 Objective: Convert units of length, capacity, and mass in the metric system.

15 On the Border Find the perimeter square ABCD: AB = 38 in. 6 square GHIJ: GH = 138 cm 7 regular hexagon BCDEFG: BC = 1 ft 3 in. 8 rectangle QRST: QR = 159 cm, RS = 49 cm 9 parallelogram WXYZ: XY= 2 ft 7 in., YZ = 1 ft 8 in. 10 regular pentagon GHIJK: JK = 1,350 mm 11 rectangle MNPQ: MN = 4 ft 7 in., MQ = 19 in. 12 rhombus JKLM: LM = 105 cm Remember! To convert from inches (a small unit) to feet (a larger unit), divide by m 4.16 m 12 ft 8 in. 12 ft 4 in. 7 ft 6 in m 5.52 m 6 m 6 ft 7 in. 8 ft 6 in. 4.1 m 6 ft 8 in. Objective: Find the perimeter of a 2-dimensional figure. 13

16 Using Measures Find the perimeter of the triangle rounded to the nearest whole number. Use the Pythagorean theorem to find the length of c. Find the perimeter of the triangle. So, the perimeter of the triangle is about 14 ft. c 2 = a 2 + b 2 c 2 = (3 ft) 2 + (5 ft) 2 c 2 = 9 ft ft 2 c = c = 5.8 ft, or 6 ft rounded to the nearest whole number. P = a + b + c P = 3 ft + 5 ft + 6 ft P = 14 ft Find the perimeter of the section rounded to the nearest foot. 1 section M 2 section N 3 section O 4 section P 5 section Q 6 section R 14

17 Remember! You may have to divide the sections into smaller parts to find the area of the whole section. Find the area in square feet of the section. 7 section M 8 section N 9 section O 10 section P 11 section Q 12 section R 87,200 1,160 90,000 1, ,000 1,340 72,000 1,605 1,280 62,400 1, ,000 Objective: Solve a problem involving measures by using data from a diagram. 15

18 It s a Cover-Up Find the area of the parallelogram. Use the formula for the area of a parallelogram. Area = base height (A = b h). So, the area of the parallelogram is 336 in. 2 base = 23 in. + 5 in. = 28 in. A = b h = 28 in. 12 in = 336 in. 2 Find the area of the parallelogram or rectangle parallelogram: b = 1 ft 8 in., h = 15 in. 6 parallelogram: b = 0.9 m, h = 25 cm 7 rectangle: b = 0.75 ft, h = 1 ft 10 in. 8 parallelogram: b = 1.2 m, h = 19 cm 9 parallelogram: b = 1.5 ft, h = 21 in. 10 rectangle: b = 24 in., h = 2.5 ft 11 parallelogram: b = 45 cm, h = 16 cm 12 rectangle: b = 1.4 m, h = 0.4 m Remember! The height of a parallelogram is always perpendicular to the base. 812 cm in cm in in. 2 5,600 cm in in cm in. 2 2,280 cm 2 2,250 cm 2 16 Objective: Find the area of a rectangle or a parallelogram.

19 Half the Work Find the area of the triangle. Determine the lengths of the base and height. b = 7 cm + 34 cm = 41 cm h = 24 cm Use the formula for the area of a triangle: Area = 1 2 base height A = 1 2 bh So, the area of the triangle is 492 cm 2. A = 1 2 bh = cm 24 cm = 492 cm 2 Find the area of the triangle cm 12 cm 13 cm 5 cm 5 NBA 6 BCN 7 AJF 8 DEF 9 HFI 10 ANC 11 FLM 12 AKM 24 cm 2 20 cm cm 2 78 cm cm 2 22 cm cm cm 2 90 cm cm cm cm 2 Objective: Find the area of a triangle. 17

20 Areas of Trapezoids You can think of a trapezoid as half a parallelogram. b 2 b 1 = base 1, b 2 = base 2, h = height Since the area of the parallelogram is (b 1 + b 2 )h, the area of the trapezoid is (b 1 + b 2 )h 2 b 1 b 2 Find the area of the trapezoid b 1 = 14 in., b 2 = 1 ft 5 in., h = 4 in. 9 b 1 = 26 cm, b 2 = 0.4 m, h = 12 cm 11 b 1 = 130 mm, b 2 = 18 cm, h = 8 cm 8 b 1 = 12.5 in., b 2 = 20.5 in., h = 0.5 ft 10 b 1 = 0.25 ft, b 2 = 8 in., h = 5 in. 12 b 1 = 3 ft, b 2 = 1 ft, h = 10 in. 240 in in in in cm cm 2 80 cm 2 99 in in cm in cm 2 18 Objective: Find the area of a trapezoid.

21 Going Around In... Find the circumference of the circle rounded to the nearest tenth. Use π Use the formula for the circumference of a circle: Circumference = 2 π radius C = 2πr C = 2πr or = 2 π 17 cm Circumference = π diameter cm C = πd So, the circumference rounded to the nearest tenth is cm. Find the circumference of the circle rounded to the nearest tenth. Use π cm 5 r = 390 mm 6 r = 1 ft 4 in. 7 d = 0.7 m 8 r = 33 cm 9 d = 46 in. 10 d = 2 ft 10 in. 11 r = 430 mm 12 d = 1 2 ft cm in in in in cm cm in in cm cm cm Objective: Find the circumference of a circle. 19

22 Circular Thinking Find the area rounded to the nearest tenth. Use π Use the formula for the area of a circle: A = πr 2 Area = π radius radius cm 7 cm A = πr cm 2 So, the area is approximately cm 2. Find the area rounded to the nearest tenth. Use π d = 2 ft 2 in. 8 r = 150 mm 9 d = 1.5 ft 10 d = 0.6 m 11 r = 22.8 cm 12 d = ft in cm 2 1,133.5 cm 2 1,632.3 cm in. 2 2,826 cm cm in cm in in cm 2 20 Objective: Find the area of a circle.

23 Parts Sectioned Off Find the area of the section rounded to the nearest whole number. Use π Find the area as if the entire figure is completed. A = πr (10 cm) cm 2 Divide the missing parts. Area of quarter circle = 1 4 πr (3.14) (10 cm) cm 2 79 cm 2 So, the area of the section is approximately 79 cm 2. Find the area of the section(s) rounded to the nearest whole number. Use π N 3 N, O, and P 5 O, M, and S 7 N, P, R, and T 9 N, M, and T 11 N, O, P, Q, R, S, and T 2 N and O 4 M 6 M and Q 8 O, M, S, and Q 10 P, Q, and R 12 O and S 1,554 cm 2 3,323 cm 2 1,960 cm cm 2 2,268 cm 2 1,190 cm 2 2,977 cm 2 3,416 cm 2 2,091 cm 2 1,035 cm 2 1,017 cm 2 3,285 cm 2 Objective: Find the area of an irregular figure by combining the areas of its parts. 21

24 Diagram Data The diagram shows how one square mile of property is divided. Each section is called a parcel. Find the area in square feet. 1 parcel II 2 a parcel made up of I and IV 3 a parcel made up of VIII, IX, and X 4 a parcel made up of XIII, XIV, and XV 5 a parcel made up of VII, XII, XIII, and XIV 6 a parcel made up of V, VIII, X, and XI Remember! 1 mi = 5,280 ft 1 acre = 43,560 ft 2 22

25 Which parcels have an area of: 7 193,600 yd 2? 8 96,800 yd 2? 9 48,400 yd 2? 10 How many square yards are there in one acre? How many acres are there in a parcel made up of the following sections? 11 I and IV 12 IV, V, and VIII 3,484,800 IV, V, VI VIII, IX, X, 2,613,600 XIV, XV 4,356,000 VII XI, XII, XIII, XVI 4,840 1,742,400 3,920, ,227, Objective: Solve a problem by using data from a diagram. 23

26 Block Party Find the surface area of the rectangular prism. Each edge is 1 in. Look at the figure from above. You see 4 in. 2 Therefore, the bottom must be 4 in. 2 Look at the figure from the front. You see 8 in. 2 Therefore, the back must be 8 in. 2 Look at the figure from the right. You see 2 in. 2 Therefore, the left must be 2 in. 2 So, the surface area of the figure is 28 in. 2 Find the surface area of the cube or rectangular prism. Area of top and bottom: 2 4 in. 2 = 8 in. 2 Area of front and back: 2 8 in. 2 = 16 in. 2 Area of right and left: 2 2 in. 2 = 4 in. 2 Total area: 28 in cm 1 cm 1 cm 1 cm 1 cm 1 cm 1 cm 1 cm 5 cube: 1 cm on each edge 7 cube: 3 cm on each edge 9 prism: l = 15 in., w = 12 in., h = 2 in. 11 cube: 4 cm on each edge 1 cm 1 cm 1 cm 1 cm 6 prism: l = 6 in., w = 9 in., h = 3 in. 8 prism: l = 8 in., w = 6 in., h = 4 in. 10 cube: 5 cm on each edge 12 prism: l = 1 ft 2 in., w = 8 in., h = 3 in. 468 in cm 2 32 cm in cm 2 48 cm 2 96 cm 2 6 cm in in cm 2 54 cm 2 24 Objective: Find the surface area of a rectangular prism.

27 Rolling Along Find the surface area of the cylinder rounded to the nearest whole number. Use π Use the formula for the surface area of a cylinder: Surface area = 2πr 2 + 2πr h where r is the radius of the base and h is the height of the cylinder. SA = 2πr 2 + 2πrh 2(3.14)(12 cm) 2 + 2(3.14) (12 cm)(15 cm) 2, cm 2 So, the surface area of the cylinder is approximately 2,035 cm 2. Find the surface area of the cylinder rounded to the nearest whole number. Use π base: r = 11 cm, h = 14 cm 7 base: d = 26 cm, h = 0.19 m 9 base: d = 0.3 m, h = 0.17 m 11 base: r = 1 ft 1 in., h = 9 in. 6 base: r = 16 in., h = 8 in. 8 base: d = 1 ft 2 in., h = 10 in. 10 base: r = 0.12 m, h = 8 cm 12 base: d = 240 mm, h = 18 cm 791 in cm 2 2,412 in. 2 1,407 cm in. 2 3,014 cm 2 2,612 cm 2 1,507 cm 2 2,261 cm in. 2 1,796 in. 2 1,727 cm 2 Objective: Find the surface area of a cylinder. 25

28 Volumes of Prisms Find the volume of the prism. Use the formula for the volume of a prism: Volume = area of base height V = B H So, the volume of the prism is 252 in. 3 V = BH, where B = 1 2 bh V = (9 in. 4 in.) 2 14 in. = 252 in. 3 Find the volume of the prism rectangular: l = 1 ft, w = 0.75 ft, h = 2 ft 2 in. 7 triangular: b = 14 in., h = 10 in., H = 1 ft 9 triangular: b = 1 ft 4 in., h = 0.5 ft, H = 1 ft 3 in. 11 rectangular: l = 2 ft, w = 5 in., h = ft 6 rectangular: l = 18 in., w = 1 ft 3 in., h = 1 2 ft 8 triangular: b = 0.25 m, h = 16 cm, H = 0.4 m 10 rectangular: l = 1 ft, w = 1 ft, h = 1 ft 12 rectangular: l = 19 in., w = 9 in., h = ft 1,620 in. 3 8,000 cm 3 1,920 cm 3 1,728 in cm 3 2,160 in. 3 2,565 in in in cm 3 2,808 in in Objective: Find the volume of a rectangular or triangular prism.

29 Volumes of Cylinders Find the volume of the cylinder rounded to the nearest whole number. Use π Use the formula for the volume of a cylinder. Volume = area of the base height. V = πr 2 h V = πr 2 h 3.14(3 ft) 2 (7 ft) ft 3 So, the volume of the cylinder is approximately 198 ft 3. Find the volume of the cylinder rounded to the nearest whole number. Use π r = 16 in., h = 10 in. 8 d = 18 cm, h = 130 mm 11 r = 3 4 ft, h = ft 6 r = 6 cm, h = 12 cm 9 d = 0.12 m, h = 14 cm 12 d = 220 mm, h = 13 cm 7 r = 1 ft 4 in., h = 0.5 ft 10 r = 10 in., h = 1 ft 6 in. 4,939 cm 3 3,306 cm 3 1,583 cm 3 1,846 in. 3 5,652 in. 3 4,823 in. 3 4,069 cm 3 1,356 cm 3 8,038 in. 3 3,815 in. 3 3,617 cm 3 6,359 in. 3 Objective: Find the volume of a cylinder. 27

30 Egyptian or Mexican Design? Find the volume of the pyramid rounded to the nearest whole number. Use the formula for the volume of a pyramid: V = 1 3 BH Volume = 1 3 area of the base height = 1 3 (9 in. 8 in.)(7 in.) V = 1 3 BH = 1 3 (504 in.3 ) So, the volume of the pyramid is 168 in. 3 = 168 in. 3 Find the volume of the pyramid rounded to the nearest whole number cm cm 9 cm 11 cm 8 cm 6 cm 10 cm 5 B = 84 cm 2, H = 8 cm 7 B = 74.6 cm 2, H = 0.15 m 9 a pyramid with a square base 13 cm on a side and height is 15 cm 11 a pyramid whose base is a right triangle with legs 9 cm and 12 cm, and height is 10 cm 6 B = in. 2, H = in. 8 B = 122 in. 2, H = 6 in. 10 a pyramid whose base is a triangle with area 45 in. 2 and height is 20 in. 12 a pyramid whose base is a rectangle with length 24 in. and width 16 in. and whose height is 1 ft 268 cm cm in cm 3 3,227 in in cm cm in cm 3 1,536 in in Objective: Find the volume of a pyramid.

31 One Scoop or Two? Find the volume of the cone rounded to the nearest whole number. Use π Use the formula for the volume of a cone: V = 1 3 πr2 h Volume = 1 3 area of a circle height 1 3 (3.14)(9 in.)2 (13 in.) V = 1 3 πr 2 h 1, in. 3 So, the volume of the cone is approximately 1,102 in. 3 Find the volume of the cone rounded to the nearest whole number. Use π cm 26 cm 5 area of base = in. 2, h = 9 in. 7 r = 14 in., h = 5 in. 9 d = 1 ft 8 in., h = 1 ft 11 d = 2 ft, h = 1 ft 6 area of base = cm 2, h = 6 cm 8 r = 30 mm, h = 17 cm 10 d = 18 cm, h = 0.18 m 12 r = 14 cm, h = 220 mm 1,026 in. 3 1,526 cm in. 3 1,809 in. 3 4,513 cm cm 3 8,470 in cm 3 1,256 in. 3 8,308 in. 3 3,919 cm cm 3 Objective: Find the volume of a cone. 29

32 Using a Model You may wish to draw a model of the information to help you. Solve the problem. 1 How many minutes will it take to cut a 15-ft piece of wood into five 3-ft sections if each cut takes 4 min? 2 How many minutes will it take to cut a 20-ft piece of pipe into four 5-ft sections if each cut takes 5 min? 3 How many square feet will be in the largest rectangle that can be formed from 24 ft of fencing? 4 If each side of the rectangle described in question 3 is increased by 3 ft, by how many square feet will the area increase? 5 A rectangular garden is to be fenced. Posts are placed every 3 ft. If 12 total posts are used and the width of the garden is 6 ft, how many square feet are in the area of the garden? 6 If the gardener decides to keep the size and shape of the garden unchanged, but places posts every 2 ft, how many posts will be needed? 7 What is the greatest number of 3 in. by 6 in. rectangles that can be cut from a sheet of cardboard that is 3 ft by 6 ft? 30

33 8 There are 25 marbles arranged in a square at the bottom of a pyramid. How many marbles are in the entire pyramid? 9 How many marbles will be in the bottom layer when there are 8 layers? 10 A pegboard in the shape of a square has 11 pegs in each row. If the area of the smallest square that can be made on the board is 1 square unit, how many square units is the largest square? 11 A school bus leaves its garage, drives west for 8 mi, north for 3 mi, east for 2 mi, south for 5 mi, east for 12 mi, and finally, north 2 mi to school. How many miles from the garage is the school now? 12 A straight cut through a rectangle makes 2 sections. What is the greatest number of sections that can be made by 4 straight cuts? Objective: Solve a problem by using a model of the figure. 31

34 Volumes of Irregular Figures Find the volume of the figure rounded to the nearest whole number. Use π Determine the basic figures that make up the irregular figure. Find the volumes of the basic figures in. 3 5,220 cm cm 3 1,693 in. 3 1,232 cm 3 4,494 cm 3 6,120 in in. 3 2,736 in. 3 1,340 in. 3 5,769 cm in Objective: Find the volume of an irregular figure by combining the volume of its parts.

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36 Getting Started with Four Easy Steps Make VersaTiles Simple to Use! Set up your VersaTiles Answer Case by placing the numbered tiles in order from 1 12 in the top 2 rows. Now you are ready to begin your activity. 1 Answer Questions Complete each question by placing the number tile on the letter in the Answer Case that corresponds to the correct answer. 2 close and flip Close the Answer Case and flip it over. Open the case and look at the pattern on the tiles. 3 match Check the tile pattern against the pattern in the Activity Book. If it matches, all answers are correct. If not, remove tiles that do not match and flip the case over again. 4 learn Rethink the incorrect answer and flip the Answer Case over again. Once the pattern in the case and the book match, the activity has been successfully completed! hand2mind.com Connect with us.