6th Grade Math Textbook, Fundamentals

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11-9

Key Concept

VBhor Vr^2 h, where

Barea of the base,

rradius of the base, and

hheight of the cylinder.

Volume (V) of a Cylinder

Volume of Cylinders and Cones

Objective To use formulas to find the volumes of cylinders and cones • To find unknown

dimensions given the volumes of cylinders and cones

A cylindrical tank is 25-feet deep and has a diameter of 110 feet.

How many cubic feet of water will the tank hold?

To find how much water, find the volume of the cylinder.

When you found the volume of a prism, you calculated the

area of the prism’s base and then multiplied it by the

prism’s height. You can also think about the volume of a

cylinder by considering its base and height.

h

r

To find the volume of the tank, use the formula. You can do this

either in terms of or by using an approximation for .

Volume of the pool (in terms of ) Volume of the pool (using 3.14 for )

V Bh V Bh

(r^2 )h (r^2 )h

(• 55^2 )25 (3.14 • 55^2 )25

(3025)25 (9498.5)25

75,625 237,462.5

So the tank will hold 75,625ft^3 , or about 237,462.5 ft^3 , of water.

Find the volume, in terms of , of a cylinder with

a radius of 7 mm and a height of 22 mm.

V Bh

(r^2 )h

(• 7^2 )22

(49)22

 1078 

So the cylinder has a volume of 1078cubic millimeters.

1

Remember:When you use either

3.14 or for , your answer will

be an approximation so you should

use the symbol. You can use the

symbol when you find volume in

terms of .

22

7

Think

The radius is half the

diameter. So r55 ft.