Question

find the volume of each hemisphere. round to the nearest tenth. (example 4) 4. 16 in. 5. 15 mm

Explanation:

Step1: Recall the formula for the volume of a hemisphere

The volume formula for a hemisphere is \(V=\frac{2}{3}\pi r^{3}\).

Step2: Solve for problem 4

Given \(r = 16\) in.
Substitute \(r = 16\) into the formula:
\(V=\frac{2}{3}\pi(16)^{3}\)
\(=\frac{2}{3}\pi\times4096\)
\(=\frac{8192}{3}\pi\)
\(\approx\frac{8192}{3}\times3.14\)
\(=\frac{25722.88}{3}\)
\(\approx8574.3\) in³

Step3: Solve for problem 5

Given \(r = 15\) mm.
Substitute \(r = 15\) into the formula:
\(V=\frac{2}{3}\pi(15)^{3}\)
\(=\frac{2}{3}\pi\times3375\)
\(= 2250\pi\)
\(\approx2250\times3.14\)
\(=7065.0\) mm³

Answer:

1. \(8574.3\) in³
2. \(7065.0\) mm³