Question

What is the volume of a hemisphere with a diameter of 8 cm, rounded to the nearest

tenth of a cubic centimeter?

Answer 1

so we know the diameter is 8 units, thus its radius is half that, or r = 4.

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies \stackrel{\textit{whole sphere}}{V=\cfrac{256\pi }{3}} \\\\\\ \stackrel{\textit{a hemisphere is half of that}}{\cfrac{256\pi }{3}\cdot \cfrac{1}{2}\implies \cfrac{128\pi }{3}}\approx 134.0412865531645\implies \stackrel{\textit{rounded up}}{134.0}`