Basic Mathematics for College Students

832 Chapter 9 An Introduction to Geometry

If an exact answer contains p, we can use 3.14 as an

approximation, and complete the calculations by hand.

Or, we can use a calculator that has a pi key to find

an approximation.

p

Note that the volume formulas for a cone, cylinder,

and sphere contain a factor of p.

Cone

Cylinder

Sphere V^43 Pr^3

VPr^2 h

V^13 Pr^2 h

Find the volume of the cylinder shown here.

Give the exact answer and an approximation

to the nearest hundredth.

Since a radius is one-half of the diameter of

the circular base,. To find

the volume of the cylinder, proceed as follows:

This is the formula for the volume of a cylinder.

Substitute 4 for r,the radius of the base, and

3 for h,the height.

Evaluate the exponential expression.

Write the product so that Pis the last factor.

Use a calculator to do the multiplication.

The exact volume of the cylinder is 48pyd^3. To the nearest

hundredth, the volume is 150.80 yd^3.

150.7964474

 48 p

Vp(16)(3)

Vp( 4 )^2 ( 3 )

Vpr^2 h

r^12 8 yd4 yd

Find the volume of the sphere shown here. Give

the exact answer and an approximation to the

nearest tenth.

This is the formula for the

volume of a sphere.

Substitute 6 for r,the radius of the sphere.

Evaluate the exponential expression.

Multiply: 4(216) 864.

Divide:.

Use a calculator to do the multiplication.

The volume of the sphere is exactly 288pft^3. To the nearest tenth,

this is 904.8 ft^3.

904.7786842

864

 288 p 3  288



864

3

p



4

3

p(216)

V

4

3

p( 6 )^3

V

4

3

pr^3

3 yd

8 yd

6 ft