If the sphere shown above has a radius of 12 units, then what is the volume of the sphere?

A.
2,880π cubic units
B.
1,152π cubic units
C.
576π cubic units
D.
2,304π cubic units

1 answer

The volume \( V \) of a sphere is given by the formula:

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

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

Given that the radius \( r = 12 \) units, we can substitute this value into the formula:

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

Now, calculate \( 12^3 \):

\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1,728 \]

Substituting this back into the volume formula:

\[ V = \frac{4}{3} \pi (1,728) \]

Now, multiply \( 1,728 \) by \( \frac{4}{3} \):

\[ V = \frac{4 \times 1,728}{3} = \frac{6,912}{3} = 2,304 \]

Therefore, the volume of the sphere is:

\[ V = 2,304\pi \text{ cubic units} \]

The correct answer is:

D. \( 2,304\pi \) cubic units