Question

Find the volume of a sphere with a radius of 12

Answer 1

The volume \( V \) of a sphere can be calculated using the formula:

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

where \( r \) is the radius of the sphere. For a sphere with a radius of 12, we can substitute \( r = 12 \) into the formula:

\[
V = \frac{4}{3} \pi (12)^3
\]

First, calculate \( 12^3 \):

\[
12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728
\]

Now substitute \( 1728 \) back into the volume formula:

\[
V = \frac{4}{3} \pi (1728)
\]

Now multiply \( 1728 \) by \( \frac{4}{3} \):

\[
V = \frac{4 \times 1728}{3} = \frac{6912}{3} = 2304
\]

So the volume of the sphere is:

\[
V = 2304 \pi
\]

If you want a numerical approximation, using \( \pi \approx 3.14 \):

\[
V \approx 2304 \times 3.14 \approx 7238.88
\]

Therefore, the volume of the sphere is:

\[
V = 2304 \pi \quad \text{or approximately} \quad 7238.88
\] cubic units.