Question

What is the volume of this sphere?

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

8 yd

cubic yards

Answer 1

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

\[
V = \frac{4}{3} \pi r^3
\]

where \( V \) is the volume and \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 8 yards, you can find the radius by dividing the diameter by 2:

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

Now, plug the radius into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (4)^3
\]

First, calculate \( (4)^3 \):

\[
4^3 = 64
\]

Now substitute this value back into the formula:

\[
V = \frac{4}{3} \times 3.14 \times 64
\]

Now, multiply \( 3.14 \times 64 \):

\[
3.14 \times 64 = 200.96
\]

Now, calculate \( \frac{4}{3} \times 200.96 \):

\[
\frac{4}{3} \times 200.96 = \frac{803.84}{3} \approx 267.95
\]

So, the volume \( V \) of the sphere is approximately \( 267.95 \) cubic yards when rounded to the nearest hundredth.

Thus, the final answer is:

\[
\text{Volume} \approx 267.95 \text{ cubic yards}
\]