Question

what is the volume of a hemisphere with a diameter of 41.6 m, rounded to the nearest tenth of a cubic meter?

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter $d$. Given $d = 41.6$ m, so $r=\frac{d}{2}=\frac{41.6}{2}=20.8$ m.

Step2: Use the volume - formula for a hemisphere

The volume $V$ of a hemisphere is given by $V=\frac{2}{3}\pi r^{3}$. Substitute $r = 20.8$ m into the formula:
$V=\frac{2}{3}\pi(20.8)^{3}$.
First, calculate $(20.8)^{3}=20.8\times20.8\times20.8 = 8998.912$.
Then, $V=\frac{2}{3}\pi\times8998.912$.
$V=\frac{2\times8998.912\pi}{3}\approx\frac{2\times8998.912\times3.14159}{3}$.
$2\times8998.912\times3.14159 = 2\times28274.337=56548.674$.
$V=\frac{56548.674}{3}\approx18849.6$.

Answer:

$18849.6$ m³