Question

calculating the volume of a sphere given diamete
what is the volume of a sphere with a radius of \\( \frac { 3 } { 2 } \\) feet?
the volume is \\( \square \pi \mathrm { ft } ^ { 3 } \\).

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(r\) is the radius of the sphere.

Step2: Substitute the given radius into the formula

Given \(r = \frac{3}{2}\) feet. Then \(r^{3}=(\frac{3}{2})^{3}=\frac{3\times3\times3}{2\times2\times2}=\frac{27}{8}\).
Substitute into the formula: \(V=\frac{4}{3}\pi\times\frac{27}{8}\).

Step3: Simplify the expression

\(\frac{4}{3}\times\frac{27}{8}=\frac{4\times27}{3\times8}=\frac{108}{24}=\frac{9}{2}\).

Answer:

\(\frac{9}{2}\)