Question

question
what is the volume of a hemisphere with a diameter of 41.6 m, rounded to the nearest tenth of a cubic meter?
answer answer 3 out of 3
18815.9
m³ submit answer

Explanation:

Step1: Find the radius

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

Step2: Use the volume formula for a hemisphere

The volume formula for a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. The volume of a hemisphere $V_{hemisphere}=\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3}$.
Substitute $r = 20.8$ m into the formula:
$V=\frac{2}{3}\pi(20.8)^{3}=\frac{2}{3}\pi\times8998.912$.
$V=\frac{17997.824\pi}{3}\approx\frac{17997.824\times3.14159}{3}$.
$V=\frac{56584.737}{3}\approx18861.6$ m³. Rounding to the nearest tenth gives $18861.6$ m³.

Answer:

$18861.6$ m³