Volume of Prisms and Cylinders
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1 Name Date Teacher Practice A Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth of a unit. Prism: V = Bh. Cylinder: V = π 2 r h. Use 3.14 for π A rectangular box measures 6 ft by 8 ft by 2 ft. Explain whether doubling a side from 6 ft to 12 ft would double the volume of the box. 11. A can of vegetables is 4.5 in. high and has a diameter of 3 in. Find the volume of the can to the nearest tenth of a unit. Use 3.14 for π. 12. A telephone pole is 30 ft tall with a diameter of 12 in. Jacob is making a replica of a telephone pole and wants to fill it with sand to help it stand freely. Find the volume of his model, which has a height of 30 in. and a diameter of 1 in., to the nearest tenth of a unit. Use 3.14 for π. Original content Copyright by EduPro, Inc.
2 Name Date Teacher CODE Practice B Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 π A cylinder has a radius of 6 ft and a height of 25 ft. Explain whether tripling the height will triple the volume of the cylinder. 11. Contemporary American building bricks are rectangular blocks with the standard dimensions of about 5.7 cm by 9.5 cm by 20.3 cm. What is the volume of a brick to the nearest tenth of a unit? 12. Find the volume of the figure. Original content Copyright by EduPro, Inc.
3 Practice C Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 π Find the missing measure to the nearest tenth. Use 3.14 π. 4. volume is 1152 ft 3 5. volume is cm 3 6. volume is 39, in 3 7. Atmo s Theater s large-sized popcorn container is a cylinder with a diameter of 9 in. and is 6 in. tall. The medium-sized container has a diameter of 6 in. and is 8 in. tall. Find the difference in the volumes. 8. The Blackmans have a new 10-ft by 20-ft rectangular swimming pool in their backyard. It has a uniform depth of 5 ft. What is the volume of water needed to fill the pool? 9. Donna decorated a three-tiered cake for her parent s anniversary party. The bottom tier had a 12-in. diameter, the middle tier, a 9-in. diameter, and the top tier, a 6-in. diameter. Each tier was 4 in. tall. What was the total volume of the cake to the nearest tenth of a unit? 10. A company produces 100,000 boxes of cereal with dimensions of 12 in. (height) by 8 in. by 1.5 in. The manufacturer is trying to cut production cost per box so the height of the box is decreased by one inch. Approximately how many more boxes of cereal can be produced in a month with the new dimensions using the same amount of cereal? Round the answer to the nearest integer.
4 Review for Mastery Volume of Prisms and Cylinders Volume = number of cubic units inside a solid figure To find the volume of this solid figure: Count the number of cubic centimeters in one slice of the figure. 4 3 = 12 Multiply by the number of slices = 72 cm 3 Complete to find the volume of each solid figure number in 3 in a slice number cm 3 in a slice = = = = number of slices = number of slices = volume = cm 3 volume = in 3 3. number mm 3 in a slice = = number of slices = volume = mm 3
5 LESSON 8-5 Review for Mastery Volume of Prisms and Cylinders (continued) Prism: solid figure named for the shape of its two congruent bases Volume V of a prism = area of base B height h V = Bh V = (6 4)5 V = 24(5) V = 120 in 3 Complete to find the volume of each prism. 4. rectangular prism 5. cube 6. triangular prism base is a rectangle base is a base is a V = Bh V = Bh V = 1 2 Bh V = ( ) V = ( ) V = 1 2 ( ) = cm 3 = mm 3 = ft 3 Cylinder: solid figure with a circular base Volume V of a cylinder = area of base B height h V = Bh V = (π 4 2 )7 = (16π)7 V = 112π V 112(3.14) units 3 Complete to find the volume of the cylinder. 7. V = Bh V = (π ) V = units 3
6 Challenge Looking Askance So far, you have considered prisms in which the outside edges are perpendicular to the plane of the base. Now, you will consider prisms in which the outside edges are not perpendicular to the plane of the base. 1. Explain why these two prisms have the same volume. A prism can have any polygon as its base. Consider an oblique prism with a base that is a parallelogram. To find the volume of this prism, first look at parallelogram JKLM which is the base of the prism. 2. How long is JK, the base of parallelogram JKLM? JK = 3. Find MQ, the height of parallelogram JKLM. Explain your method. MQ = 4. What is the area of the base of the prism? B = 5. Find KR, the height of the prism. Explain your method. KR = 6. Find the volume of the prism. V =
7 Problem Solving Volume of Prisms and Cylinders Round to the nearest tenth. Write the correct answer. 1. A contractor pours a sidewalk that is 4 inches deep, 1 yard wide, and 20 yards long. How many cubic yards of concrete will be needed? (Hint: 36 inches = 1 yard.) 2. A refrigerator has inside measurements of 50 cm by 118 cm by 44 cm. What is the capacity of the refrigerator? A rectangular box is 2 inches high, 3.5 inches wide and 4 inches long. A cylindrical box is 3.5 inches high and has a diameter of 3.2 inches. Use 3.14 for π. Round to the nearest tenth. 3. Which box has a larger volume? 4. How much bigger is the larger box? Use 3.14 for π. Choose the letter for the best answer. 5. A child s wading pool has a diameter of 5 feet and a height of 1 foot. How much water would it take to fill the pool? Round to the nearest gallon. (Hint: 1 cubic foot of water is approximately 7.5 gallons.) A 79 gallons C 59 gallons B 589 gallons D 147 gallons 7. How many gallons of water will the water trough hold? Round to the nearest gallon. (Hint: 1 cubic foot of water is approximately 7.5 gallons.) 6. How many cubic feet of air are in a room that is 15 feet long, 10 feet wide and 8 feet high? F 33 ft 3 G 1200 ft 3 H 1500 ft 3 J 3768 ft 3 8. A can has diameter of 9.8 cm and is 13.2 cm tall. What is the capacity of the can? Round to the nearest tenth. F cm 3 G cm 3 H cm 3 J cm 3 A 19 gallons B 71 gallons C 141 gallons D 565 gallons
8 Reading Strategies Using a Model Volume is the amount of space a solid figure occupies. Volume is measured in cubic units. One cubic unit A rectangular prism is a three-dimensional figure. The length, width, and height are the measures that make up the three dimensions. You can find the volume of a rectangular prism by multiplying the length times the width times the height. The formula for the volume of a rectangular prism is: V = h. Use the rectangular prism to complete Exercises How long is the prism? 2. How wide is the prism? 3. What is the height of the prism? 4. Write the formula you will use to find the volume of this prism. 5. Rewrite the formula with values for each dimension of the prism. 6. What is the volume of this prism?
9 Puzzles, Twisters & Teasers Turn Up the Volume! Across 2. A is a three-dimensional figure named for the shape of its bases. 4. The volume of a prism or cylinder is expressed in units. 6. The volume of a prism can be written as V = h. 9. The volume of a prism is the area of the times the height. Down 1. The of a three-dimensional figure is the number of cubic units needed to fill it. 3. The area of the base of a prism or cylinder is expressed in units. 5. The volume of a is the area of the base times the height. 7. To find the volume of a three-dimensional figure, find the volume of each part and add the volumes together. 8. If all six faces of a rectangular prism are squares, it is a. LESSON 8-5
10 ANSWER Practice A ft in in m in ft m cm ft The original box has a volume of 96 ft 3. You could double the volume to 192 ft 3 by doubling any one of the dimensions in in 3 Practice B 1. 10,164 in cm m cm m ,608 cm in m ft 3 Possible answer: 10. The original cylinder has a volume of 2826 ft 3. If you triple the height the volume is 8478 ft 3, which is triple the original volume cm ft 3 Practice C 1. 21,362.4 cm ft ,843.4 in ft cm in in ft in boxes Review for Mastery 1. 4; 2; 8; ; 15; 2; 4; ; 30; 4. 8; 6; 4; 4; square; 6. right ; 3; 3; 3; 3; 4; 27 6; ; 3; 75π; Challenge 1. Areas of bases are equal; heights are equal units 3. 4 units; Pythagorean Theorem = 36 units units; Pythagorean Theorem = 432 units 3 Problem Solving yd ,600 cm 3 3. Cylinder in 3 5. D 6. G 7. B 8. G Reading Strategies 1. 3 units 2. 2 units 3. 3 units 4. V = h 5. V = cubic units Puzzles, Twisters & Teasers Across 2. prism 4. cubic 6. rectangular 9. base Down 1. volume 3. square 5. cylinder 7. composite 8. cube
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