Exercise 3 Page 616

We are given a cylinder and we want to find its volume.

To calculate the volume of a cylinder, we can use the following formula.

V = π r^{2} h

In this formula,

r

is the radius of the base and

h

is the height of the cylinder. From the diagram above we can see that the diameter of the base is

24

meters. Recall that the diameter of a circle is twice the radius. With this in mind, we can find the radius by substituting

d = 24

into the formula below.

d = 2 r

$d = 24$

24 = 2 r

$LHS / 2 = RHS / 2$

\frac{2 4}{2} = \frac{2 r}{2}

$\frac{a}{b} = \frac{a / 2}{b / 2}$

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

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

12 = r

Rearrange equation

r = 12

Finally, by substituting

r

with

12

and

h

with

42

into the formula for the volume, we can solve for

V .

Let's do it!

V = π r^{2} h

$r = 12$ , $h = 42$

V = π 12^{2} (42)

▼

Evaluate right-hand side

Calculate power

V = π 144 (42)

V = π (6048)

Use a calculator

V = 19000.35236891 \dots

Round to $1$ decimal place(s)

V \approx 19000.4

The approximate volume of the given cylinder is

19000.4

cubic meters.