Question

The diameter, D, of a sphere is 10.4 m. Calculate the sphere's volume, V.

Use the value 3.14 for n, and round your answer to the nearest tenth.
(Do not round any intermediate computations)

Answer 1

To calculate the volume \( V \) 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 \( r \) from the diameter \( D \). The radius is half of the diameter:

\[
r = \frac{D}{2} = \frac{10.4 \, \text{m}}{2} = 5.2 \, \text{m}
\]

Now we can substitute \( r \) into the volume formula. Using \( \pi \approx 3.14 \), we have:

\[
V = \frac{4}{3} \times 3.14 \times (5.2)^3
\]

Next, we need to compute \( (5.2)^3 \):

\[
(5.2)^3 = 5.2 \times 5.2 \times 5.2
\]

Calculating step by step:

1. \( 5.2 \times 5.2 = 27.04 \)
2. \( 27.04 \times 5.2 = 140.608 \)

Now we can substitute \( (5.2)^3 \) back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 140.608
\]

Next, calculate \( 3.14 \times 140.608 \):

\[
3.14 \times 140.608 \approx 442.07952
\]

Now we multiply by \( \frac{4}{3} \):

\[
V = \frac{4}{3} \times 442.07952
\]

Calculating this gives:

\[
V \approx 589.43936
\]

Finally, rounding to the nearest tenth:

\[
V \approx 589.4 \, \text{m}^3
\]

Thus, the volume of the sphere is approximately \( \text{589.4 m}^3 \).