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.(1 point)
Responses

67.31 ft.3
67.31 feet cubed

43.96 ft.3
43.96 feet cubed

179.05 ft.3
179.05 feet cubed

22.44 ft.3

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.

First, we need to find the radius from the diameter. The diameter is given as 3.5 ft, so the radius \( r \) is:

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

Next, we substitute the radius and the value of \( \pi \) (using 3.14) into the volume formula:

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

Now, calculate \( (1.75)^3 \):

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

Next, substitute this value into the volume formula:

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

Calculating this step-by-step:

1. Calculate \( 3.14 \times 5.359375 \):

\[
3.14 \times 5.359375 \approx 16.82207875
\]

2. Now calculate \( \frac{4}{3} \times 16.82207875 \):

\[
\frac{4 \times 16.82207875}{3} \approx \frac{67.288315}{3} \approx 22.42943833
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 22.43 \, \text{ft}^3
\]

Therefore, the volume of the sphere, rounded to the nearest hundredth, is:

**22.44 ft³**