Math Practice Use a Formula

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1 9.4 Volumes of Prisms How can you find te volume of a prism? ACTIVITY: Pearls in a Treasure Cest Work wit a partner. A treasure cest is filled wit valuable pearls. Eac pearl is about centimeter in diameter and is wort about $80. Use te diagrams below to describe two ways tat you can estimate te number of pearls in te treasure cest. a. cm 60 cm b. 20 cm 60 cm c. Use te metod in part (a) to estimate te value of te pearls in te cest. 2 Geometry In tis lesson, you will find volumes of prisms. solve real-life problems. ACTIVITY: Finding a Formula for Volume Work wit a partner. You know tat te formula for te volume of a rectangular prism is V = ℓw. a. Write a formula tat gives te volume in terms of te area of te base and te eigt. b. Use bot formulas to find te volume of eac prism. Do bot formulas give you te same volume? 376 Capter 9 ms_red pe_0904.indd 376 Surface Area and Volume 2/2/5 9:7:43 AM

2 3 ACTIVITY: Finding a Formula for Volume Mat Practice Use a Formula Wat are te given quantities? How can you use te quantities to write a formula? Work wit a partner. Use te concept in Activity 2 to find a formula tat gives te volume of any prism. Triangular Prism Rectangular Prism Pentagonal Prism Triangular Prism Hexagonal Prism Octagonal Prism 4 ACTIVITY: Using a Formula Work wit a partner. A ream of paper as 500 seets. a. Does a single seet of paper ave a volume? Wy or wy not? b. If so, explain ow you can find te volume of a single seet of paper. 5. IN YOUR OWN WORDS How can you find te volume of a prism? 6. STRUCTURE Draw a prism tat as a trapezoid as its base. Use your formula to find te volume of te prism. Use wat you learned about te volumes of prisms to complete Exercises 4 6 on page 380. Section 9.4 Volumes of Prisms 377

3 9.4 Lesson Lesson Tutorials Te volume of a tree-dimensional figure is a measure of te amount of space tat it occupies. Volume is measured in cubic units. Remember Te volume V of a cube wit an edge lengt of s is V = s 3. Volume of a Prism Words Te volume V of a prism is te product of te area of te base and te eigt of te prism. area of base, eigt, area of base, eigt, Algebra V = Area of base Heigt of prism EXAMPLE Finding te Volume of a Prism Study Tip Te area of te base of a rectangular prism is te product of te lengt and te widt w. You can use V = w to find te volume of a rectangular prism. Find te volume of te prism. V = Write formula for volume. = 6(8) 5 Substitute. = 48 5 Simplify. = 720 Multiply. Te volume is 720 cubic yards. 6 yd 8 yd 5 yd EXAMPLE 2 Finding te Volume of a Prism Find te volume of te prism. V = = 2 (5.5)(2) 4 Substitute. = Simplify. = 22 Multiply. Te volume is 22 cubic inces. Write formula for volume. 2 in. 5.5 in. 4 in. 378 Capter 9 Surface Area and Volume

4 Exercises 4 2 Find te volume of te prism ft 4 ft 4 ft 5 m 2 m 9 m 3 in. EXAMPLE ag A 3 ag 4 in. 4 in. 4 in. Real-Life Application A movie teater designs two bags to old 96 cubic inces of popcorn. (a) Find te eigt of eac bag. (b) Wic bag sould te teater coose to reduce te amount of paper needed? Explain. a. Find te eigt of eac bag. ag A V = ag V = 96 = 4(3)() 96 = 4(4)() 96 = 2 96 = 6 8 = 6 = Te eigt is 8 inces. Te eigt is 6 inces. b. To determine te amount of paper needed, find te surface area of eac bag. Do not include te top base. ag A S = w w ag S = w w = 4(3) + 2(4)(8) + 2(3)(8) = 4(4) + 2(4)(6) + 2(4)(6) = = = 24 in. 2 = 2 in. 2 Te surface area of ag is less tan te surface area of ag A. So, te teater sould coose ag. 3. You design ag C tat as a volume of 96 cubic inces. Sould te teater in Example 3 coose your bag? Explain. ag C 4 in. 4.8 in. Section 9.4 Volumes of Prisms 379

5 9.4 Exercises Help wit Homework. VOCAULARY Wat types of units are used to describe volume? 2. VOCAULARY Explain ow to find te volume of a prism. 3. CRITICAL THINKING How are volume and surface area different? 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= Find te volume of te prism in m 2 9 in. 9 in. 8 cm 6 cm 2 cm 4 m 7 m 7. 8 yd 3 6 yd 4 yd ft 4.5 ft 9 ft 9. 0 mm 0.5 mm 8 mm m 7.2 m 0 m 5 mm 43 mm 2 20 ft 66 ft 2 3. ERROR ANALYSIS Describe and correct te error in finding te volume of te triangular prism. Scool Locker 7 cm 5 cm 0 cm V = = 0(5)(7) = 50 7 = 350 cm 3 Gym Locker 60 in. 48 in. 4. LOCKER Eac locker is saped like a rectangular prism. Wic as more storage space? Explain. 2 in. 2 in. 5. CEREAL OX A cereal box is 9 inces by 2.5 inces by 0 inces. Wat is te volume of te box? 0 in. 5 in. 380 Capter 9 Surface Area and Volume

6 Find te volume of te prism ft 2 in. 30 ft 2 in. 0 in. 20 ft 8. LOGIC Two prisms ave te same volume. Do tey always, sometimes, or never ave te same surface area? Explain. 9. CUIC UNITS How many cubic inces are in a cubic foot? Use a sketc to explain your reasoning. 6 in. 20. CAPACITY As a gift, you fill te calendar wit packets of cocolate candy. Eac packet as a volume of 2 cubic inces. Find te maximum number of packets you can fit inside te calendar. 8 in. 4 in. 2. PRECISION Two liters of water are poured into an empty vase saped like an octagonal prism. Te base area is 00 square centimeters. Wat is te eigt of te water? ( L = 000 cm 3 ) 22. GAS TANK Te gas tank is 20% full. Use te current price of regular gasoline in your community to find te cost to fill te tank. ( gal = 23 in. 3 ) in..25 ft.75 ft 23. OPEN-ENDED You visit an aquarium. One of te tanks at te aquarium olds 450 gallons of water. Draw a diagram to sow one possible set of dimensions of te tank. ( gal = 23 in. 3 ) 24. How many times greater is te volume of a triangular prism wen one of its dimensions is doubled? wen all tree dimensions are doubled? w Find te selling price. (Section 6.6) 25. Cost to store: $ Cost to store: $ Cost to store: $30 Markup: 20% Markup: 60% Markup: 85% 28. MULTIPLE CHOICE Wat is te approximate surface area of a cylinder wit a radius of 3 inces and a eigt of 0 inces? (Section 9.3) A 30 in in. 2 C 27 in. 2 D 245 in. 2 Section 9.4 Volumes of Prisms 38