Question

What number can be used to complete the volume statement for the cone?

A cone with height 4 meters and diameter 3 meters.

Volume =
Pi meters cubed

Answer 1

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

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.

Given:
- The height \( h = 4 \) meters,
- The diameter of the cone is \( 3 \) meters. Therefore, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{3 \, \text{meters}}{2} = 1.5 \, \text{meters}
\]

Now substituting the values into the volume formula:

\[
V = \frac{1}{3} \pi (1.5)^2 (4)
\]

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now substituting this back into the formula:

\[
V = \frac{1}{3} \pi (2.25)(4)
\]

Calculating \( 2.25 \times 4 \):

\[
2.25 \times 4 = 9
\]

Now substituting that into the volume formula:

\[
V = \frac{1}{3} \pi (9) = 3 \pi
\]

So, the volume of the cone is:

\[
V = 3 \pi \, \text{meters cubed}
\]

Therefore, the number to complete the volume statement for the cone is:

\[
\boxed{3}
\]