Chapters 11 and 12 Study Guide Name: Length, Area, Surface Area, Block: and Volume of Solids
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1 Page 1 of 15 Chapters 11 and 12 Study Guide Name: Length, Area, Surface Area, Block: and Volume of Solids SOL G.13 The student will use formulas for surface area and volume of three-dimensional objects to solve real-world problems. SOL G.14 The student will use similar geometric objects in two- or three-dimensions to: a) compare ratios between side lengths, perimeters, areas, and volumes; b) determine how changes in one or more dimensions of an object affect area and/or volume of the object; c) determine how changes in area and/or volume of an object affect one or more dimensions of the object; and d) solve real-world problems about similar geometric objects. Block / Date Section and Objectives Find areas of triangles, parallelograms, trapezoids, rhombuses, and kites Determine the perimeter and area for similar polygons Determine the circumference and arc length for a circle Determine the surface are of prisms, cylinders, pyramids, and cones Determine the volume of prisms, cylinders, pyramids, and cones Review 4 Test Classwork and Homework Pg 780 # 5 20 Pg 784 # 1 16 Ch. 11 Rvw worksheet Check answer key Pg 916 # 2 24, (evens only!!) Ch 12 Review Packet #1 Check answer key Ch 12 Review Packet #2 WS on Ratios for Polygons and 3-D Figures Check answer key SOL Testing Dates: May 19: Block 3 Eat A lunch Room 6 May 20: Block 8 Eat A lunch Room 121 May 22: Block 5 Bring a snack Electronic Classroom Helpful Hints Review your notes daily. Need extra practice? Do the odds in the back of the text and check your answers. Come to class with specific questions. Include all drawings and show the work that leads to your solution for all problems. For each problem: write formula, include substitution, and write answer. Include units.
2 Page 2 of 15 Geometry Name Date Pd Area Formulas Square - A = s 2 Trapezoid - A = 1 b ) Rectangle - A = bh or lw Rhombus - A = dd Parallelogram - A = bh Kite - A = dd Triangle - A = 1 bh 2 Examples: 1. Find the area of parallelogram PQRS. Q 4 R 12 T 8 P 6 S U 2. The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and the height. Q 3. Find the area of the rhombus. 9 mm P 12 mm R S Similar Polygons b Ratio of corresponding sides (perimeter) is a:b Ratio of area is a 2 :b 2 a I II 4. In the diagram, ABC DEF. Find the indicated ratio. Poly gon I ~ Poly gon II a. ratio (ABC to DEF) of the perimeters b. ratio (ABC to DEF) of the areas A B F 8 12 C E D
3 Page 3 of 15 Circumference of a Circle - C = 2 r or C = d 5. Find the indicated measure. a. circumference of a circle with radius 9 inches b. radius of a circle with circumference 26 meters arc length A length or arc AB = mab 2 r 360 Find the length of each arc. P r B 6. AB 7. EF 8. GH A E 11 cm 8 cm P 60 Q 60 G 11 cm 120 R B F H Area of a Circle - A = r 2 9. Find the indicated measure. a. area of a circle whose radius is 2.5 cm b. diameter of a circle whose area is cm 2 Area of a Sector area of sector APB = mab 360 r 2 P r B A 10. Find the area of each sector 11. Find the area of circle V. S T 70 8 V U T V 40 A = 35m 2 U
4 Page 4 of 15 Geometry Ch.11 Rvw Name Date Pd Areas square: rectangle: parallelogram: triangle: trapezoid: rhombus: kite: circle: circumference (of a circle): arc length: sector: **Round answers to two decimal places when necessary. 1. Find the area of a square that is 8.5 in on a side. 2. Find the area of a triangle that has a base of 4 cm and a height of 9 cm. 3. Find the area of a circle that has a diameter of 10 yd. 4. Find the area of a trapezoid that has bases of 55 cm and 22 cm and a height of 21 cm.
5 Page 5 of 15 Find the area of each figure. Video solution for #5 and # m m 4.2 in m 19 cm 9 cm 17 cm cm 4.1 y d 6 cm 8.5 y d
6 Page 6 of mm 15.2 cm 5.4 cm in 23.7 in 4 km in in 17 y d 52 in 23 y d
7 Page 7 of 15 In circle D shown below, EDF FDG. Find the indicated measure. 17. length of arc EFG H 18. length of arc EHG D E 80 G 7m 19. length of arc FEG F Find the area of BOTH the sectors formed by ACB. #20 has a video solution (7:20) B 20. A D 4 in. C 65 B 130 C 27 cm B D C m A D A Check your solutions:
8 Page 8 of 15 Geometry Ch.12 Packet #1 Name Date Pd Show all work!!!!! Use Euler s Theorem to find the value of n. 1. Faces: n 2. Faces: 5 3. Faces: 8 Vertices: 8 Vertices: 6 Vertices: n Edges: 12 Edges: n Edges: 18 Find the number of faces, vertices, and edges of the polyhedron Find the surface area of the right prism. Round your answer to two decimal places Find the surface area of the right cylinder. Round your answer to two decimal places
9 Page 9 of 15 Find the surface area of the regular pyramid. Round your answer to two decimal places Find the surface area of the right cone. Round your answer to two decimal places Find the volume of the right prism or right cylinder. Round your answer to two decimal places
10 Page 10 of 15 Find the volume of the pyramid. Round your answer to two decimal places Find the volume of the cone. Round your answer to two decimal places Find the surface area of the sphere. Round your answer to two decimal places Find the volume of the sphere. Round your answer to two decimal places Check your solutions:
11 Page 11 of 15 Geometry Ch. 12 Packet #2 Name Date Pd Find the surface area of the following figures. Round your answers to two decimals places
12 Page 12 of Find the volume of each figure. Round answers to two decimal places
13 Page 13 of Check your solutions:
14 Page 14 of 15 Chapter 11 and 12 WS on Ratios for Polygons and 3-D Figures Check your solutions Complete the table of ratios for similar polygons. Ratio of corresponding side lengths Ratio of perimeters Ratio of areas 1. 5:8 2. 4: : :18 Corresponding lengths in similar figures are given. Find the ratios (shaded to unshaded) of the perimeters and areas. Find the unknown area The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. 7. Ratio of areas = 16:81 8. Ratio of areas = 25:196
15 Page 15 of 15 Complete the table of ratios for similar solids. Scale factor Ratio of areas Ratio of volumes 9. 5: : : :3 Solid A (shown) is similar to Solid B (not shown) with the given scale factor of A to B. Find the surface area and volume of Solid B. 13. Scale factor of 3:2 Surface Area Volume 14. Scale factor of 2:1 Surface Area Volume 15. Scale factor of 4:7 Surface Area Volume 16. Two similar cylinders have volumes 12 cubic units and 324 cubic units. Find the scale factor of the smaller cylinder to the larger cylinder.
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