Question

what is the volume of the sphere in terms of \\(\pi\\)? \\(v = \square\pi\\ \text{in.}^3\\) (the sphere has a radius of 6 in. as shown in the image)

Explanation:

Step1: Identify the radius

The diameter of the sphere is 6 inches, so the radius \( r = \frac{6}{2} = 3 \) inches.

Step2: Use the volume formula for a sphere

The formula for the volume \( V \) of a sphere is \( V = \frac{4}{3}\pi r^3 \). Substitute \( r = 3 \) into the formula:
\[
V = \frac{4}{3}\pi (3)^3
\]

Step3: Calculate \( (3)^3 \)

\( 3^3 = 27 \), so the formula becomes:
\[
V = \frac{4}{3}\pi \times 27
\]

Step4: Simplify the expression

\( \frac{4}{3} \times 27 = 36 \), so \( V = 36\pi \) cubic inches.

Answer:

36