12-5 Volume of Prisms
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1 Find the volume of each figure. 1. Find the volume of each figure mm m 3 90 yd in 3 4. A window box has a length of 8.5 inches and a height of 9 inches. If the volume of the box is 2295 cubic inches, what is the width of the box? 30 in. 5. Find the volume of the figure shown ft ft in 3 54 in 3 esolutions Manual - Powered by Cognero Page 1
2 Josh and his mom are building the dog house shown. Find the volume of the dog house. 984 mm ,300 in cm triangular prism: base of triangle 6.2 yards, height of triangle 20 yards, height of prism 14 yards 868 yd rectangular prism: height 4 inches, width 1 inches, length 1 in 3 inch 17. Morgan is building a model of some steps with 6-inch foam blocks. What is the total volume of the blocks? 3888 in Jill is mailing a candle that is in the shape of a triangular prism as shown. She put the candle in a rectangular box that measures 3 inches by 5 inches by 7 inches and places foam pieces around the candle. Find the volume of the foam pieces needed to fill the space between the candle and the box. 14. Find the length of a rectangular prism with a width of 4 feet, a height of 6 feet, and a volume of 84 cubic feet. 3.5 ft 15. Find the height of a triangular prism with a base length of 10 yards, a base height of 20 yards, and a volume of 600 cubic yards. 6 yd 85.5 in The height of a triangular prism is 8 feet and it has a volume of 200 cubic feet. If the base has a length of 5 feet, what is the height of the base? 10 ft esolutions Manual - Powered by Cognero Page 2
3 20. Ben wants to buy enough potting soil to fill a window box that is 42 inches long, 8 inches wide, and 6 inches high. If one bag of potting soil contains 576 cubic inches, how many bags should he buy? 25. A chocolate bar is in the shape of a trapezoidal prism as shown. Find the volume of the chocolate bar. 4 bags Find the volume of each figure m in Financial Literacy A movie theater sells different sizes of popcorn as shown in the table. If the containers are rectangular prisms, find the ratio of cost to the volume of each bag of popcorn. Which size of popcorn is the best buy? cm 3 small: $0.03 per in 3, medium: $0.02 per in 3, large: $0.01 per in 3 ; The large popcorn is the best buy per cubic inch ft ft 3 esolutions Manual - Powered by Cognero Page 3
4 27. Make a Conjecture Refer to the figure. a. What is the volume of the figure? b. How does the volume change if one of the dimensions are doubled? two dimensions? three dimensions? Explain. c. Repeat the above steps and triple each dimension. What do you notice? d. Without calculating, say how the volume of the prism changes if each of the dimensions is multiplied by 6. a. 42 cm 3 b. The original volume is multiplied by 2 because.; The original volume is multiplied by 2 2 or 4 because.; The original volume is multiplied by 2 3 or 8 because. c. When one dimension is tripled, the volume is multiplied by 3. When two dimensions are tripled, the original volume is multiplied by 3 2. When three dimensions are tripled, the original volume is multiplied by 3 3. d. The volume is multiplied by Justify Conclusions Without calculating, compare the volumes of the prisms shown. Explain your reasoning to a classmate. 29. Persevere with Problems Find the dimensions of any triangular prism that has a volume of 44 cubic inches. Sample answer: base length 4 in., base height 2 in., prism height 11 in. Persevere with Problems Use dimensional analysis to make each conversion yd 3 = ft ft 3 = yd m 3 = cm 3 2,000, Building on the Essential Question Explain how doubling the length, width, and height of a box changes the volume of the box. The volume is multiplied by 2 3 or Mr. Toshio is filling a 20-foot by 35-foot garden framed by two levels of bricks with topsoil. If the topsoil costs $9 per cubic foot, what other information is needed to find s, the cost of the soil? A the area of the garden B the perimeter of the garden C the price per cubic yard of soil D the height of the bricks Sample answer: The volumes are equal. The length of each figure is the same. The width of the first figure is twice the width of the second figure and the height of the first figure is half the height of the second figure. So, the volumes are the same. D esolutions Manual - Powered by Cognero Page 4
5 35. Short Response How many centimeters tall is a rectangular prism with a length of 8 centimeters, width of 10 centimeters, and a volume of 960 cubic centimeters? What is the volume of the prism shown? mm Tomás wants to spend less than $100 for a new soccer ball and shoes. The ball costs $24. Write and solve an inequality that gives the amount that Tomás can spend on shoes. F 67.5 ft 3 G 90 ft 3 H 108 ft 3 J 216 ft 3 H 37. Which of the following is the best estimate for the volume of a shoe box with sides that measure inches, 9.25 inches, and 8 inches? A 10 in 3 B 100 in 3 C 1000 in 3 D 10,000 in s < 100; less than $76 Find each sum or difference. Write in simplest form. C Find the area of each figure. Round to the nearest tenth yd esolutions Manual - Powered by Cognero Page 5
6 mi Kristin bought a scarf on sale for 25% off the original price of $40. The sales tax on the scarf was 7.5%. What was the total price of the scarf, including tax? $ A shirt is on sale for 40% off the original price of $35. What is the sale price? $21 Find the area of each circle. Round to the nearest tenth in m 2 esolutions Manual - Powered by Cognero Page 6
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