Question
What is the volume of a sphere with a radius of 3/2 feet?
The volume is
Pi ft3.
The volume is
Pi ft3.
Answers
Answered by
GPT-4o mini
The formula for the volume \( V \) of a sphere with radius \( r \) is given by:
\[
V = \frac{4}{3} \pi r^3
\]
For a sphere with a radius of \( r = \frac{3}{2} \) feet, we can calculate the volume as follows:
1. Calculate \( r^3 \):
\[
r^3 = \left(\frac{3}{2}\right)^3 = \frac{3^3}{2^3} = \frac{27}{8}
\]
2. Substitute \( r^3 \) into the volume formula:
\[
V = \frac{4}{3} \pi \left(\frac{27}{8}\right)
\]
3. Simplify the expression:
\[
V = \frac{4 \cdot 27}{3 \cdot 8} \pi = \frac{108}{24} \pi = \frac{9}{2} \pi
\]
Thus, the volume of the sphere is:
\[
\frac{9}{2} \pi \text{ ft}^3
\]
\[
V = \frac{4}{3} \pi r^3
\]
For a sphere with a radius of \( r = \frac{3}{2} \) feet, we can calculate the volume as follows:
1. Calculate \( r^3 \):
\[
r^3 = \left(\frac{3}{2}\right)^3 = \frac{3^3}{2^3} = \frac{27}{8}
\]
2. Substitute \( r^3 \) into the volume formula:
\[
V = \frac{4}{3} \pi \left(\frac{27}{8}\right)
\]
3. Simplify the expression:
\[
V = \frac{4 \cdot 27}{3 \cdot 8} \pi = \frac{108}{24} \pi = \frac{9}{2} \pi
\]
Thus, the volume of the sphere is:
\[
\frac{9}{2} \pi \text{ ft}^3
\]