Question
the diameter of a ball is 6in what is the volume
Answers
GPT-4o mini
To find the volume of a sphere (which is the shape of a ball), 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. The radius is half of the diameter.
Given the diameter of the ball is 6 inches, the radius \( r \) will be:
\[
r = \frac{6}{2} = 3 \text{ inches}
\]
Now, substitute the radius into the volume formula:
\[
V = \frac{4}{3} \pi (3)^3
\]
Calculating \( (3)^3 \):
\[
(3)^3 = 27
\]
Now plug that back into the equation:
\[
V = \frac{4}{3} \pi (27)
\]
\[
V = 36\pi
\]
Using \( \pi \approx 3.14 \) for an approximate value:
\[
V \approx 36 \times 3.14 \approx 113.04 \text{ cubic inches}
\]
Therefore, the volume of the ball is approximately \( 113.04 \) cubic inches.
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius of the sphere. The radius is half of the diameter.
Given the diameter of the ball is 6 inches, the radius \( r \) will be:
\[
r = \frac{6}{2} = 3 \text{ inches}
\]
Now, substitute the radius into the volume formula:
\[
V = \frac{4}{3} \pi (3)^3
\]
Calculating \( (3)^3 \):
\[
(3)^3 = 27
\]
Now plug that back into the equation:
\[
V = \frac{4}{3} \pi (27)
\]
\[
V = 36\pi
\]
Using \( \pi \approx 3.14 \) for an approximate value:
\[
V \approx 36 \times 3.14 \approx 113.04 \text{ cubic inches}
\]
Therefore, the volume of the ball is approximately \( 113.04 \) cubic inches.