Exercise 20 Page 603

We are told that a cone has a height of $9$ inches and a base whose diameter is $7 \frac{1}{2}$ inches. Let's start by drawing it.

To find the volume, we can use the formula for the volume of a cone.

V = \frac{1}{3} π r^{2} h

Here,

r

is the radius and

h

is the height of the cone. We already know that the height of the cone is

9

inches. To find

r

we can divide the diameter

d

by

2 .

r = \frac{d}{2}

$d = 7 \frac{1}{2}$

r = \frac{7 \frac{1}{2}}{2}

▼

Evaluate right-hand side

$a \frac{b}{c} = \frac{a \cdot c + b}{c}$

r = \frac{\frac{1 5}{2}}{2}

$\frac{a}{b} = \frac{1}{b} \cdot a$

r = \frac{1}{2} (\frac{1 5}{2})

Multiply fractions

r = \frac{1 5}{4}

The radius of the base is

\frac{1 5}{4}

inches. Let's substitute these values into the formula and calculate the volume.

V = \frac{1}{3} π r^{2} h

$r = \frac{1 5}{4}$ , $h = 9$

V = \frac{1}{3} π (\frac{1 5}{4})^{2} (9)

▼

Evaluate right-hand side

$(\frac{a}{b})^{m} = \frac{a ^{m}}{b ^{m}}$

V = \frac{1}{3} π (\frac{2 2 5}{1 6}) (9)

V = \frac{1}{3} π (\frac{2 0 2 5}{1 6})

Commutative Property of Addition

V = \frac{1}{3} (\frac{2 0 2 5}{1 6}) π

Multiply fractions

V = \frac{2 0 2 5}{4 8} π

Use a calculator

V = 132.535940 \dots

Round to $1$ decimal place(s)

V \approx 132.5

The volume of the cone is about

132.5

cubic inches.