11.5 Start Thinking Warm Up Cumulative Review Warm Up
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1 11.5 Start Thinking Consider the stack of coins shown in Figure A. What is the volume of the cylinder formed by the stack of coins? The same coins are stacked as shown in Figure B. What is the volume of this new cylinder? Did the height of the stack change? Did the volume change? What conclusion can you make about the volume of a cylinder, right or oblique? Figure A Figure B 11.5 Warm Up Find the volume of the solid cm 8 cm 12 in. 7 cm 15 cm 10 in. 4 cm 11.5 Cumulative Review Warm Up Use a calculator to find the trigonometric ratio. Round your answer to four decimal places. 1. sin sin 98. tan cos cos tan 10 94
2 Name Date 11.5 Practice A In Exercises 1 and 2, find the volume of the prism in. 7 in. In Exercises and 4, find the volume of the cylinder ft 9 cm 8 cm 6 yd 10 yd 5. A cylindrical container with a radius of 12 centimeters is filled to a height of 6 centimeters with coconut oil. The density of coconut oil is 0.92 gram per cubic centimeter. What is the mass of the coconut oil to the nearest gram? In Exercises 6 and 7, find the missing dimension. 6. olume = 240 m 7. olume = in. 8 m t 5 m s In Exercises 8 and 9, find the area of the base of the rectangular prism with the given volume and height. Then give a possible length and width. 8. = 9, h = 8 ft 9. = = 144 cm, h 6 cm 10. The prisms are similar. Find the volume 11. Find the volume of of Prism B. the composite solid. Prism A Prism B 4 cm 1 cm 2 cm 5 cm 8 m 6 m 7 cm 9 cm = 800 m 12. A cylindrical swimming pool is approximately 12 feet wide and 4 feet deep. About how many gallons of water does the swimming pool contain? Remember that 1 cubic foot is approximately 7.48 gallons. Copyright Big Ideas Learning, LLC Geometry 95
3 Name Date 11.5 Practice B In Exercises 1 and 2, find the volume of the prism ft 12 ft m 2.4 m In Exercises and 4, find the volume of the cylinder in in..2 m 11.8 cm m 5. A cylindrical container with a radius of 8 centimeters is filled to a height of 10 centimeters with sulfuric acid. The density of sulfuric acid is 1.84 grams per cubic centimeter. What is the mass of the sulfuric acid to the nearest gram? In Exercises 6 and 7, find the missing dimension. 6. olume = 120 ft 7. olume = m r 10 ft 9 m q In Exercises 8 and 9, find the area of the base of the rectangular prism with the given volume and height. Then give a possible length and width. 8. = 216 yd, h = 12 yd 9. = 448 in., h = The cylinders are similar. Find the volume 11. Find the volume of the composite solid. of Cylinder B. Cylinder B Cylinder A 6 in. = 112 π in. 12. An aquarium shaped like a rectangular prism has a length of 24 inches, a width of 12 inches, and a height of 18 inches. You fill the aquarium half full with water. When you submerge a rock in the aquarium, the water level rises 0.5 inch. Find the volume of the rock. 96
4 Name Date 11.5 Enrichment and Extension olumes of Prisms and Cylinders Find the volume of the three-dimensional figure in terms of x x x x + 1 x + 2 x 1. A rectangular prism has a volume of 720 cubic centimeters. Its surface area is 484 square centimeters and the edge lengths are consecutive integers. Determine the longest segment that can be drawn to connect two vertices. 4. The volume in cubic units of a cylinder is equal to its surface area in square units. Prove that the radius and height must both be greater than 2. In Exercises 5 and 6, find the volume of the right prism or right cylinder in cm In Exercises 7 9, the figure is a cylinder with an oblique face. The volume of 2 πr such a cylinder is given by = ( h1 + h2 ) Find the volume of a cylinder with an oblique face in which r = 8 centimeters, h 1 = 1 centimeters, and h 2 = 10 centimeters. 8. Find the radius of a cylinder with an oblique face in which = 00 π cubic inches, h 1 = 1 inches, and h 2 = 11 inches. h 2 r h 1 9. Find h 2 of a cylinder with an oblique face in which = 88π cubic feet, r = 4 feet, and h 1 = 6 feet. Copyright Big Ideas Learning, LLC Geometry 97
5 Name Date 11.5 Puzzle Time What Starts With A P, Ends With An E, And Has One Million Letters In It? Write the letter of each answer in the box containing the exercise number. Complete the sentence. 1. The of a solid is the number of cubic units contained in its interior. 2. Principle states that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.. is the amount of matter that an object has per unit volume. Find the volume in square feet of the figure. Round your answer to the nearest hundredth. 9 ft ft 6. 7 ft 22 ft 20 ft 4 ft Answers E. volume I. 6 J. area O P. Shepherd s Q. 16 S. 24 T. 5 F. Cavalieri s C. 2 Find the value of the variable. 7. z m m = m 1 = 204 ft 10. An element has a volume of 20.2 cubic centimeters and a mass of grams. Find the density (in grams per cubic centimeter). u ft 14 cm 11 cm = 770 cm w cm D. mass E F. 15 O. 240 P T. density U F. 10 G P
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Name Class Date 19. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Resource Locker Explore Developing a Surface Area Formula Surface
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