Question

question 10 of 42 what is the volume of the sphere shown below with a radius of 6? a. 288π cu units b. 144π cu units c. 162π cu units d. 48π cu units

Explanation:

Step1: Recall the formula for the volume of a sphere.

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

Step2: Substitute the given radius \( r = 6 \) into the formula.

First, calculate \( r^3 \): \( 6^3 = 6\times6\times6 = 216 \).
Then, multiply by \( \frac{4}{3}\pi \): \( V=\frac{4}{3}\pi\times216 \).
Simplify \( \frac{4}{3}\times216 \): \( \frac{4\times216}{3}=4\times72 = 288 \).
So, \( V = 288\pi \) cubic units. Wait, but looking at the options, maybe there was a typo? Wait, no, let's check again. Wait, maybe I misread the options. Wait, the options: A is 288π? Wait, the user's image: Option A: 288π cu units? Wait, maybe the original problem's options, let's recheck. Wait, the user's image: Option A: 288π cu units? Wait, maybe I made a mistake. Wait, radius 6: \( \frac{4}{3}\pi r^3=\frac{4}{3}\pi\times216 = 288\pi \). So the correct answer should be A (if A is 288π). Wait, the user's options: A. 288π cu units? Let's check the options again. The user's image:

Options:

A. 288π cu units

B. 144π cu units

C. 162π cu units

D. 48π cu units

So step by step:

1. Formula: \( V = \frac{4}{3}\pi r^3 \)

1. Substitute \( r = 6 \):

\( r^3 = 6^3 = 216 \)

\( V=\frac{4}{3}\pi\times216 = 4\times72\pi = 288\pi \)

Answer:

A. 288π cu units