what is the volume of a hemisphere with a diameter of 7.6 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. Given $d = 7.6$ m, so $r=\frac{d}{2}=\frac{7.6}{2}=3.8$ 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 $r = 3.8$ m into the formula: $V=\frac{2}{3}\pi(3.8)^{3}=\frac{2}{3}\pi\times54.872$. $V=\frac{109.744\pi}{3}\approx\frac{109.744\times3.14159}{3}$. $V=\frac{344.717}{3}\approx114.9$ m³.

Answer:

$114.9$ m³