9.4 Volume of Prisms and Cylinders
9.4 Volume of Prisms and Cylinders 9.4 Volume of Prisms and Cylinders
Careers AQUARIUM DIVER In addition to feeding and taking care of the fish and the plants in an aquarium, divers make sure that the tank does not get too crowded. Volume of a Cylinder Find the volume of the cylinder. Round your answer to the nearest whole number. 27. 4 in. 28. 6 m 29. Swimming Pools In Exercises 30–32, find the volume of the pool. Round your answer to the nearest whole number. Then compare the volumes of the pools to answer Exercise 33. 30. 20 ft 31. 24 ft 32. 4 ft 4 ft 3 ft 33. Which pool above requires the least amount of water to fill it? Visualize It! In Exercises 34 and 35, use the information below. Suppose that a 3-inch by 5-inch index card is rotated around a horizontal line and a vertical line to produce two different solids. 3 in. 9 in. 5 in. 34. Find the volume of each solid. 35. Which solid has a greater volume? Explain your reasoning. Aquariums In Exercises 36 and 37, use the information below. The Giant Ocean Tank at the New England Aquarium is a cylinder that is 23 feet deep and 40 feet in diameter as shown. 23 ft 36. Find the volume of the tank. 37. How many gallons of water are needed to fill the tank? (1 ft 3 ≈ 7.5 gal) 15 ft 38. Personal Aquariums To avoid overcrowding in a personal aquarium, you should buy one fish for every gallon of water (231 in. 3 ≈ 1 gal). About how many fish should be in an aquarium that is a rectangular prism measuring 20 inches wide, 10 inches long, and is filled with water to a height of 11 inches? 3 in. 5 in. 40 ft 12 m 9.4 Volume of Prisms and Cylinders 505
IStudent Help I CLASSZONE.COM HOMEWORK HELP Extra help with problem solving in Exs. 41–43 is at classzone.com You be the Judge Find the volume of the passenger car of the Space Spiral at Cedar Point Amusement Park in Sandusky, Ohio. Solution The passenger car is a cylinder with a “hole” in it. To find the volume, subtract the volume of the hole from the volume of the larger cylinder. Volume of larger cylinder πr 2 h π(10 2 )(14) ≈ 4398 Volume of “hole” πr 2 h π(4 2 )(14) ≈ 704 ANSWER The volume of the passenger car is about 4398 704 3694 cubic feet. In Exercises 39 and 40, use the cartons shown. 39. Find the volume of each carton of ice cream. 40. Terry assumes that because the dimensions doubled, the jumbo carton contains twice as much ice cream as the regular carton. Is Terry right? Explain your reasoning. Finding Volume In Exercises 41–43, find the volume of the solid. 41. 2 in. 1 in. 42. 8 ft 43. 1 m 3 ft 6 in. 506 Chapter 9 Surface Area and Volume EXAMPLE Find Volume Using Algebra Write an expression for the volume of the solid in terms of x. 44. 45. 46. x 3 x 4 2 in. 8 in. x 2x 10 cm 10 ft 7 Cool 5 cm 20 cm 3x 14 ft 4 m JUMBO JUMBO Cool 10 ft 4 ft 5x 4 m 10 cm 4 m
- Page 1 and 2: Goal Find the volumes of prisms and
- Page 3 and 4: 502 Chapter 9 Surface Area and Volu
- Page 5: IStudent Help I CLASSZONE.COM HOMEW
IStudent Help<br />
I CLASSZONE.COM<br />
HOMEWORK HELP<br />
Extra help with problem<br />
solving in Exs. 41–43 is<br />
at classzone.com<br />
You be the Judge<br />
Find the volume <strong>of</strong> the passenger car <strong>of</strong> the<br />
Space Spiral at Cedar Point Amusement Park<br />
in S<strong>and</strong>usky, Ohio.<br />
Solution<br />
The passenger car is a cylinder with a “hole” in it.<br />
To find the volume, subtract the volume <strong>of</strong> the hole<br />
from the volume <strong>of</strong> the larger cylinder.<br />
<strong>Volume</strong> <strong>of</strong> larger cylinder πr 2 h<br />
π(10 2 )(14)<br />
≈ 4398<br />
<strong>Volume</strong> <strong>of</strong> “hole” πr 2 h<br />
π(4 2 )(14)<br />
≈ 704<br />
ANSWER The volume <strong>of</strong> the passenger car is<br />
about 4398 704 3694 cubic feet.<br />
In Exercises 39 <strong>and</strong> 40, use the cartons shown.<br />
39. Find the volume <strong>of</strong> each carton <strong>of</strong> ice cream.<br />
40. Terry assumes that because the<br />
dimensions doubled, the jumbo<br />
carton contains twice as much ice<br />
cream as the regular carton. Is<br />
Terry right? Explain your reasoning.<br />
Finding <strong>Volume</strong> In Exercises 41–43, find the volume <strong>of</strong> the solid.<br />
41. 2 in. 1 in. 42. 8 ft 43. 1 m<br />
3 ft<br />
6 in.<br />
506 Chapter 9 Surface Area <strong>and</strong> <strong>Volume</strong><br />
EXAMPLE Find <strong>Volume</strong><br />
Using Algebra Write an expression for the volume <strong>of</strong> the solid in<br />
terms <strong>of</strong> x.<br />
44. 45. 46. x<br />
3<br />
x<br />
4<br />
2 in.<br />
8 in.<br />
x<br />
2x<br />
10 cm<br />
10 ft<br />
7<br />
Cool<br />
5 cm<br />
20 cm<br />
3x<br />
14 ft<br />
4 m<br />
JUMBO JUMBO<br />
Cool<br />
10 ft 4 ft<br />
5x<br />
4 m<br />
10 cm<br />
4 m
Change language