Question

what is the volume of a hemisphere with a diameter of 8ft (rounded to the nearest tenth of a cubic foot)

Answer 1

well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.

`\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}`