Question

an igloo can be modeled as a hemisphere. its radius measures 4.4 m. find its volume in cubic meters. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the formula for the volume of a hemisphere

The volume \(V\) of a hemisphere is given by \(V=\frac{2}{3}\pi r^{3}\), where \(r\) is the radius.

Step2: Substitute the given radius into the formula

Given \(r = 4.4\) m. Then \(V=\frac{2}{3}\pi(4.4)^{3}\).
First, calculate \((4.4)^{3}=4.4\times4.4\times4.4 = 85.184\).
So \(V=\frac{2}{3}\pi\times85.184\).
\(\frac{2}{3}\times85.184=\frac{170.368}{3}\approx56.7893\).
Then \(V\approx56.7893\times\pi\).
Taking \(\pi\approx3.14\), we have \(V\approx56.7893\times3.14 = 178.3184\).

Answer:

\(178.3\) cubic meters.