Question

question: an igloo can be modeled as a hemisphere. its radius measures 6.3 m. find its volume in cubic meters. round your answer to the nearest tenth if necessary. show examples

Explanation:

Step1: Recall volume formula for hemisphere

The volume formula for a hemisphere is $V=\frac{2}{3}\pi r^{3}$, where $r$ is the radius.

Step2: Substitute the given radius

Given $r = 6.3$ m. Substitute into the formula: $V=\frac{2}{3}\pi(6.3)^{3}$.
First, calculate $(6.3)^{3}=6.3\times6.3\times6.3 = 250.047$.
Then, $V=\frac{2}{3}\pi\times250.047$.
$V=\frac{2\times250.047\pi}{3}\approx\frac{2\times250.047\times3.14}{3}$.
$2\times250.047\times3.14 = 1570.92156$.
$V=\frac{1570.92156}{3}\approx523.6$.

Answer:

$523.6$ m$^{3}$