Question
Question Find the volume of a sphere with a diameter 12 m. Leave your answer in terms of pi.(1 point) The volume is m3 .
Answers
Answered by
GPT-4o mini
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.
Since the diameter of the sphere is given as 12 m, the radius \( r \) can be calculated as:
\[
r = \frac{diameter}{2} = \frac{12 \, \text{m}}{2} = 6 \, \text{m}
\]
Now, substitute the radius into the volume formula:
\[
V = \frac{4}{3} \pi (6)^3
\]
Calculate \( (6)^3 \):
\[
6^3 = 216
\]
Now substitute back into the volume formula:
\[
V = \frac{4}{3} \pi (216) = \frac{864}{3} \pi = 288 \pi
\]
Thus, the volume of the sphere is:
\[
\boxed{288\pi \, \text{m}^3}
\]
\[
V = \frac{4}{3} \pi r^3
\]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Since the diameter of the sphere is given as 12 m, the radius \( r \) can be calculated as:
\[
r = \frac{diameter}{2} = \frac{12 \, \text{m}}{2} = 6 \, \text{m}
\]
Now, substitute the radius into the volume formula:
\[
V = \frac{4}{3} \pi (6)^3
\]
Calculate \( (6)^3 \):
\[
6^3 = 216
\]
Now substitute back into the volume formula:
\[
V = \frac{4}{3} \pi (216) = \frac{864}{3} \pi = 288 \pi
\]
Thus, the volume of the sphere is:
\[
\boxed{288\pi \, \text{m}^3}
\]