Question

a sphere of radius 2 inches is cut by three planes passing through its center. this partitions the solid into 8 equal parts, one of which is shown. the volume of each part is $t\pi$ cubic inches. what is the value of $t$?

Explanation:

Step1: Calculate the volume of the sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 2\) inches, we substitute \(r\) into the formula:

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Step2: Find the volume of each part

Since the sphere is divided into 8 equal parts, we divide the volume of the sphere by 8. Let \(V_{part}\) be the volume of each part. Then \(V_{part}=\frac{\frac{32}{3}\pi}{8}\).

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Comparing \(V_{part}=t\pi\) with \(\frac{4}{3}\pi\), we can see that \(t = \frac{4}{3}\).

Answer:

\(\frac{4}{3}\)