Question

1. find the volume of the sphere. leave your answer in terms of π. type a response

Explanation:

Step1: Recall the volume formula for a sphere

The formula for the volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere. From the diagram, the radius \( r = 15\space mm \).

Step2: Substitute the radius into the formula

Substitute \( r = 15 \) into the formula \( V=\frac{4}{3}\pi r^{3} \). So we have \( V=\frac{4}{3}\pi(15)^{3} \).

First, calculate \( 15^{3}=15\times15\times15 = 3375 \). Then, multiply by \( \frac{4}{3} \): \( \frac{4}{3}\times3375=4\times1125 = 4500 \). So the volume \( V = 4500\pi \) cubic millimeters.

Answer:

The volume of the sphere is \( 4500\pi \) cubic millimeters.