Question

tori is painting a model of the moon for a science project. the model moon is a solid clay sphere with a volume of 3,240 cubic centimeters. what is the diameter of the model moon? round your answer to the nearest hundredth. centimeters submit

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula for a sphere is \( V=\frac{4}{3}\pi r^{3}\), where \(V\) is the volume and \(r\) is the radius.
Given \(V = 3240\space cm^{3}\), we substitute into the formula: \(3240=\frac{4}{3}\pi r^{3}\).

Step2: Solve for \(r^{3}\)

First, multiply both sides of the equation by \(\frac{3}{4}\) to get \(r^{3}\) alone on one side.
\(r^{3}=\frac{3\times3240}{4\pi}\).
Calculate \(\frac{3\times3240}{4}=2430\), so \(r^{3}=\frac{2430}{\pi}\approx\frac{2430}{3.14159}\approx773.5\).

Step3: Solve for \(r\)

Take the cube - root of \(r^{3}\). \(r=\sqrt[3]{773.5}\approx9.18\space cm\).

Step4: Calculate the diameter \(d\)

Since \(d = 2r\), then \(d=2\times9.18 = 18.36\space cm\).

Answer:

\(18.36\)