Question

bellwork 9/12/25
the moon is approximately spherical with a diameter of 2159 miles. find the volume of moon.

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter $d$. Given $d = 2159$ miles, so $r=\frac{d}{2}=\frac{2159}{2}$ miles.

Step2: Use the volume formula for a sphere

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = \frac{2159}{2}$ into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\pi(\frac{2159}{2})^{3}\\ &=\frac{4}{3}\pi\times\frac{2159^{3}}{8}\\ &=\frac{\pi\times2159^{3}}{6} \end{align*}$$

\]
\[

$$\begin{align*} 2159^{3}&=2159\times2159\times2159\\ &=(2159\times2159)\times2159\\ & = 4661281\times2159\\ &=10063705679 \end{align*}$$

\]
\[
V=\frac{\pi\times10063705679}{6}\approx\frac{3.14\times10063705679}{6}\approx 5.26\times 10^{9}\text{ cubic - miles}
\]

Answer:

Approximately $5.26\times 10^{9}$ cubic miles