Question

What is the volume of this cylinder?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

14 yd
8 yd

cubic yards

Answer 1

To find the volume of a cylinder, you can use the formula:

\[
V = \pi r^2 h
\]

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

Given:
- Height \( h = 14 \text{ yd} \)
- Diameter of the base \( d = 8 \text{ yd} \)

First, we need to find the radius \( r \), which is half of the diameter:

\[
r = \frac{d}{2} = \frac{8 \text{ yd}}{2} = 4 \text{ yd}
\]

Now we can plug the values into the volume formula:

\[
V = \pi r^2 h = 3.14 \times (4 \text{ yd})^2 \times 14 \text{ yd}
\]

Calculating \( r^2 \):

\[
(4 \text{ yd})^2 = 16 \text{ yd}^2
\]

Now substituting back into the volume formula:

\[
V = 3.14 \times 16 \text{ yd}^2 \times 14 \text{ yd}
\]

Calculating \( 16 \times 14 \):

\[
16 \times 14 = 224 \text{ yd}^3
\]

Now substituting this into the equation:

\[
V = 3.14 \times 224 \text{ yd}^3
\]

Calculating \( 3.14 \times 224 \):

\[
V \approx 703.36 \text{ yd}^3
\]

Rounding to the nearest hundredth, the volume of the cylinder is approximately:

\[
\boxed{703.36} \text{ cubic yards}
\]