Geometry: Unit 11 Rectangular Prism Notes Rectangular Prism:

Transcription

1 : Unit 11 Rectangular Prism Notes Date: Rectangular Prism: How do we find Total Area? Example 1 Find the area of each face: 6cm Front: Back: Top: 8cm Bottom: Left Side: Right Side: 10cm Total: How do you find the Lateral Area? Formula for the Formula for the Total Area of a Rectangular Prism: Example 2 Find the lateral area: Find the total area: 6m 6m 20m 9in Example 3 Find the lateral area: Find the total area: 9in 9in page 1

2 : Unit 11 Rectangular Prism Notes Date: Volume: Formula for Volume of a Rectangular Prism: Revisit Example 1: L = W = H = Find the volume: Revisit Example 2: L = W = H = Find the volume: Revisit Example 3: L = W = H = Find the volume: Example 4: Find the Lateral Area, Total Area, and Volume of the rectangular prism. 7in 5in 13in Volume: page 2

3 Unit 11 Class Practice Date: L H W Volume (V) = Area of the Base x height of the prism Lateral Area (L.A) = Perimeter x height Total Area (T.A) = Lateral Area + 2(Area of the Base) Find the lateral area, total area, and volume of each rectangular prism. 1. L = 4cm W = 3cm H = 2cm LA = TA = V = 2. L = 5m W = 3m H = 3m LA = TA = V = 3. L = 5ft W = 4ft H = 3ft LA = TA = V = 4. L = 7in W = 2in H = 4in LA = TA = V = 5. L = 3mm W = 2mm H = 6mm LA = TA = V = Example 1: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism. 12m 12m Area of the Base: 8m 7m 4m Perimeter of the Base: 8m 7m Height: 12m Total Area; Volume: Example 2: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism. 14m 10m 6m 16m 10m Total Area; Volume: page 3

4 Other Right Prisms - Notes Date: Example 3: Find the Lateral Area, Total Area and Volume of the Trapezoidal Right Prism. 30m Volume: 40m 10m 14m 18m 8m 1. 42m 24m 36m 12m 18m m 42m 24m 20m 28m 18m Page 4

5 Unit 11, Prisms Homework Date: Find the Volume, Lateral Area, and Total Area of each figure m 16m 40m 24m 28m 2. 4in 16in Base is a square m 24m 28m 20m 22m 50m Page 5

6 Unit 11, Prisms Homework Date: Find the Volume, Lateral Area, and Total Area of each figure m 5m 6m 7.5m 12.5m 2. 50mm 25mm 28mm 3. 30m 50m 60m 25m 30m 70m Page 6

7 Pyramid Notes Date: Regular Pyramid - We will be looking at square pyramids. Lateral Area - Total Area - Volume - Therefore, we need to find the following four pieces of information for each problem: Example 1 8in = h 12in = e 1. Area of the base A = e 2 2. Perimeter of the base P = 4e 3. Height h 4. Slant height - l Base Edge - Height Slant Height 10in = l Area of the base Perimeter of the base - Lateral Area - Total Area - Volume - Page 7

8 Pyramid Notes - Continued Date: Example 2 Base Edge - Height Slant Height Area of the base Perimeter of the base - Lateral Area - 24in 26in Total Area - Volume - 20in Example 3 10m Base Edge - Height Slant Height Area of the base Perimeter of the base - 12m 13m Lateral Area - Total Area - Volume - Example 4 - Base Edge - Height Slant Height Area of the base Perimeter of the base - 8ft 15ft 17ft Lateral Area - Total Area - Volume - Page 8

9 Unit 11 Pyramids Homework Date: page m 60m 22m ft 20ft 9ft 3. 25in 24in 14in mm 9mm 18mm

10 Unit 11 Pyramids Homework Date: Page m 2.3m 7m 6. 14ft 14ft 14ft ft 6ft 3ft 8. 3cm 3cm 6cm 5cm 1.7cm

11 Cylinder Notes Date: A cylinder is like the right prisms with which we have been working all week, except that the bases of a cylinder are circles. The volume and total area can be calculated in a very similar manner. In a cylinder, the formula for Volume is exactly the same. Multiply the area of the base by the height. In this case the base is a circle. Recall that the area of a circle is calculated by using A =. The Lateral Area and Total Area is calculated in a similar manner. However we must replace perimeter of base with, use Therefore, to find the Total Area and Volume of a cylinder you must still calculate the same three pieces of information: 1. of the base 2. of the base 3. Height of the object given Example 1 Find the Total Area and Volume of the given cylinder. Radius Area of Base Circumference of Base Height Volume 10in Lateral Area 4in Total Area - page 11

12 Cylinder Notes Date: Example 2 14m 7m Radius Area of Base Circumference of Base Height Volume Lateral Area - Total Area - Example 3 100cm 75cm Radius Area of Base Circumference of Base Height Volume Lateral Area - Total Area - Example 4 Radius Area of Base Circumference of Base Height 27in 22.8in Volume Lateral Area - Total Area - Page 12

13 Cones Notes Date: Cone - Volume - Lateral Area - Total Area - Therefore, now we need to find the four key pieces of information first: 1. Area of the base 2. Circumference of the base - 3. Height - 4. Slant height - Example 1 Find the Volume and Total Area Radius - Area of the base 10m Circumference of the base 8m Height - Slant height 6m Lateral Area - Total Area - Volume - page 13

14 Cones Notes - Continued Date: Example 2 Find the Volume and Total Area 15m 9m 12m Radius - Area of the base Circumference of the base Height - Slant height Lateral Area - Total Area - Volume - Example 3 Find the Volume and Total Area 26cm 24cm Radius - Area of the base Circumference of the base Height - Slant height Lateral Area - Total Area - Volume - Example 4 Find the Volume and Total Area 3in 4in Radius - Area of the base Circumference of the base Height - Slant height Lateral Area - Total Area - Volume - Page 14

15 : Unit 11 Cylinders and Cones Homework Date: 1. 47ft 13ft 2. Answers should be in feet. 2yd 24ft 3. Answers should be in inches. 5in 1ft 4. 18m 18m page 15

16 : Unit 11 Cylinders and Cones Homework Date: 1. 17in 2. 8in 24ft 20ft 3. 12cm 5cm 4. 6in 20in 20in page 16

17 : Unit 11 Sphere Notes Date: Sphere - Volume - Total Area - Example 1 Find the Total Area and Volume of the Sphere 6in Radius - Volume - Total Area - Example 2 Find the Total Area and Volume of the Sphere 15mm Radius - Volume - Total Area - page 17

18 : Unit 11 Sphere Notes Date: Example 3 Find the Total Area and Volume of the Sphere Radius - Volume - 1cm Total Area - Example 4 Find the Total Area and Volume of the Sphere Radius - Volume ft Total Area - Applications: Complete the following application problems involving circles. 1.) Since ice cream is Ms. K s favorite treat she decides to take you to Cold Stone Creamery for a tasty treat. Your server places a scoop of ice cream with a radius of 4cm on a cone with a radius of 3cm and height 15cm. It is so hot out that your ice cream begins to melt. Is the cone big enough to hold all the ice cream if it melts? 2.) A spherical fishbowl has a diameter of 24cm. To fill the fish bowl three-fourths full, about how many liters of water would you need? Give your answer to the nearest 0.1 liter. Use 3.14 for π. Note: 1000cm 3 = 1 liter. page 18

19 Unit 11 Spheres and Mixed Homework Date: 1. 4m 2. 15m 8m cm 2cm 4. 6m 7m 10m page 19

20 Unit 11 Spheres and Mixed Homework Date: ft 6. 13m 12m 10m 7. 28ft 8. 8m 4m 9m page 20

21 : Unit 11 Warm-Ups Name: Cumulative Review Date: Thursday, June 4 th : Calculate the distance, midpoint, and slope between each set of points. 2 2 x2 x1 y2 y 1 Distance: x2 x1 y2 y1 Midpoint:, Slope: (-5, 6) and (-5, -9) 2. (4, 8) and (-2, 8) y2 y1 x x 2 1 Distance: Midpoint: Slope: Distance: Midpoint: Slope: 3. (2, -6) and (5, 2) 4. (9-3) and (-9, 4) Distance: Midpoint: Slope: Distance: Midpoint: Slope: VOCABULARY REVIEW:

22 Unit 11 Warm-Ups Date: Friday, June 5 th cm 1.2cm cm 8m 4m 9m Cumulative Review: Determine the value of x and the missing segments. Label Diagrams!!

23 Unit 11 Warm-Ups Date: Monday, June 8 th 1. 17in 15in 2. 12m 18m 20m Cumulative Review: Determine the value of x and the missing angles or segments. x = x = m ABD = m ABD = m ABC = m ABC = 5. B is the midpoint of AC, AB = x + 4 and BC = 2x 5. Find x, AB, BC, and AC. x = AB= BC= AC=

24 Unit 11 Warm-Ups Date: Tuesday, June 9 th 1. 49m 14m 2. 34cm 30cm Cumulative Review: Use the properties of parallel lines to find x. 3.) a b 4.) c d 5.) e f 11x-15 10x-15 3x+12 9x+23 5x+80 5x+8 Complete the following definitions. 6. Points on the same line are called. 7. Points that lie on the same plane are called. 8. Lines that lie in the same plane and never intersect are called. 9. An angle with measure of more than 0 and less than 90 is a angle. 10. angles are two angles who measures sum to angles are two angles who measures sum to 90.

25 Unit 11 Warm-Ups Date: Wednesday, June 10 th 1. 16m 2. 24cm Cumulative Review: Classify the triangle by it s sides or angles. State which side or angles will be the largest and the smallest. 3.) 4.) 5.) Classify: Classify: Classify: Largest Angle: Longest Side: Largest Angle: Smallest Angle: Shortest Side: Smallest Angle: Cumulative Review: Find the value of x. 6.) 7.) 8.) x = x = x =

26 Unit 11 Warm-Ups Date: Thursday, June 11 th 1. 49m 14m 2. A rectangular aquarium has dimensions of 3x4x5 feet. a. Draw a diagram with labels. b. What is the name of this geometric solid? PRISM/PYRAMID/CYLINDER/CONE/SPHERE c. How much glass would be needed to make the aquarium if the base and lid are also made out of glass? d. If it costs $.15 cents per square inch of glass, how much will it cost to make the aquarium? e. How many cubic inches of water can the aquarium hold? f. If we built 10 identical aquariums, how many cubic inches of water could they hold?

27 Unit 11 Warm-Ups Date: Friday, June 12 th 1. 13m 12m 10m 2. 15cm 9cm 3. 24ft 4. 25m 10m

28 Unit 11 Warm-Ups Date: Monday, June 11 th Identify CD as a Median (M), Altitude (A), Angle Bisector (AB), or Perpendicular Bisector (PB). 1.) 2.) 3.) 4.) 5.) 6.) Decide which method(s) can be used to proof that the triangles are congruent. (SSS,ASA,SAS,AAS,HL). If there is not enough information to prove congruence, write none. 7.) 8.) 9.) Ds: DABC D Reason: Ds: DJKL D Reason: Ds: DLMN D Reason: None None None 10.) 11.) 12.) Ds: DFGH D Ds: DSTU D Ds: DABC D Reason: Reason: Reason: None None None

29 Unit 11 Warm-Ups Date: Tuesday, June 12 th Apply the properties of parallelograms to solve for the missing sides and angles. 22.) EF = ; FG = 23.) EF = ; FG = 24.) EF = ; FG = 25.) m K = ; m L = ; m M =. 26.) m K = ; m L = ; m M =. 27.) m K = ; m L = ; m J =. 28.) DE = 29.) DE = 30.) DE = Convert all measurements in the Metric or English systems. km hm dam m dm cm mm 1.) 15km = m 2.) mm = m 3.) 12.05km = mm 4.) cm = km 5.) 60 inches = ft. 6.) 6 miles = yards 7.) 72 inches = feet 8.) 23 miles = inches 20.) MN =. 21.) MN =. 22.) MN =.