Question

the large sphere has a diameter of 20 feet. which expression represents the volume, in cubic units, of the shaded part of the sphere? o $\frac{4}{3}pi(10^{3})+\frac{4}{3}pi(4^{3})$ o $\frac{4}{3}pi(10^{3})-\frac{4}{3}pi(4^{3})$ o $\frac{4}{3}pi(20^{3})+\frac{4}{3}pi(4^{3})$ o $\frac{4}{3}pi(20^{3})-\frac{4}{3}pi(4^{3})$

Explanation:

Step1: Find the radius of the large sphere

The diameter of the large sphere is 20 feet, so the radius $R = \frac{20}{2}=10$ feet.

Step2: Recall the volume - formula of a sphere

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

Step3: Determine the volume of the shaded part

The volume of the shaded part is the volume of the large sphere minus the volume of the small sphere. The radius of the small sphere is 4 feet. The volume of the large sphere is $V_{1}=\frac{4}{3}\pi(10^{3})$ and the volume of the small sphere is $V_{2}=\frac{4}{3}\pi(4^{3})$. So the volume of the shaded part is $V = \frac{4}{3}\pi(10^{3})-\frac{4}{3}\pi(4^{3})$.

Answer:

$\frac{4}{3}\pi(10^{3})-\frac{4}{3}\pi(4^{3})$