Find the volume of a sphere with a diameter 12 m. Leave your answer in terms of pi.(1 point) The volume is m3 .

1 answer

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.

Given the diameter of the sphere is 12 m, we can find the radius by dividing the diameter by 2:

\[ r = \frac{12}{2} = 6 , \text{m} \]

Now, we can substitute the radius into the volume formula:

\[ V = \frac{4}{3} \pi (6)^3 \]

Calculating \( 6^3 \):

\[ 6^3 = 216 \]

Now substituting back into the volume formula:

\[ V = \frac{4}{3} \pi (216) \]

Now, calculating \( \frac{4}{3} \times 216 \):

\[ \frac{4}{3} \times 216 = \frac{864}{3} = 288 \]

Therefore, the volume is:

\[ V = 288\pi , \text{m}^3 \]

So the volume of the sphere is \( 288\pi , \text{m}^3 \).