Question

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

Answer 1

To calculate the volume of a sphere, we use the formula:

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

where \( r \) is the radius of the sphere.

Given that the width of the sphere is 10.6 feet, this width represents the diameter. The radius \( r \) is half the diameter:

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

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

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

Calculating \( (5.3)^3 \):

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

Using \( \pi \approx 3.14 \):

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

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

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

Now, multiplying by \( 148.877 \):

\[
V \approx 4.18667 \times 148.877 \approx 623.993
\]

Rounding to the nearest hundredth:

\[
V \approx 624.00 \text{ cubic feet}
\]

So, the volume of the sphere is approximately \( \boxed{624.00} \) cubic feet.