Question

What is the volume of this sphere?
width 10.6 ft
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
______ cubic feet

Answer 1

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

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

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

The width given for the sphere is 10.6 ft, which refers to the diameter. The radius \( r \) is half of the diameter, so we can calculate the radius as follows:

\[
r = \frac{\text{diameter}}{2} = \frac{10.6 \text{ ft}}{2} = 5.3 \text{ ft}
\]

Next, we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (5.3)^3
\]

Now, we calculate \( (5.3)^3 \):

\[
5.3^3 = 5.3 \times 5.3 \times 5.3 = 148.877
\]

Now, substituting \( \pi \approx 3.14 \) into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 148.877
\]

Calculating \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]

Now multiply this by \( 148.877 \):

\[
V \approx 4.18667 \times 148.877 \approx 623.4
\]

Rounding to the nearest hundredth, we have:

\[
V \approx 623.4 \text{ cubic feet}
\]

Thus, the volume of the sphere is approximately **623.40 cubic feet**.