Question

Find the volume of a sphere with a diameter of 3.5 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.(

Answer 1

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

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

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

First, we need to find the radius from the diameter. The radius is half the diameter:

\[
r = \frac{d}{2} = \frac{3.5 \, \text{ft}}{2} = 1.75 \, \text{ft}
\]

Now we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (1.75)^3
\]

Next, we calculate \( (1.75)^3 \):

\[
(1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375
\]

Now substituting this value back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 5.359375
\]

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

\[
\frac{4}{3} \times 3.14 \approx 4.18666667
\]

Now multiply this value by \( 5.359375 \):

\[
V \approx 4.18666667 \times 5.359375 \approx 22.435
\]

Rounding to the nearest hundredth:

\[
V \approx 22.44 \, \text{ft}^3
\]

Therefore, the volume of the sphere is approximately \( \boxed{22.44} \, \text{ft}^3 \).