Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

To find the volume of a sphere, you can use the formula:

\[

V = \frac{4}{3} \pi r^3

\]

In this case, the radius (r) is given as 3. Substituting this value into the formula gives:

\[

V = \frac{4}{3} \pi (3)^3

\]

Calculating \( (3)^3 \) results in 27, so the expression for the volume becomes:

\[

V = \frac{4}{3} \pi \cdot 27

\]

Now, multiplying that out:

\[

V = \frac{4 \cdot 27}{3} \pi = \frac{108}{3} \pi = 36 \pi

\]

Thus, the volume of the sphere when the radius is 3 is \( 36 \pi \), which corresponds to the option provided. This shows how to correctly apply the volume formula for a sphere and perform calculations involving exponents and fractions effectively.