Question

A hemispherical tank has a total surface area of 243pi ft^2 (this includes the circular base area) Find the volume Please help!!

Answer 1

The surface area of a sphere is
\[ A_{sphere} = 4\pi r^2\]
in this case, a hemisphere is just half a sphere.
So it is
\[A_{hemisphere} =2 \pi r^2 \]

So we solve for r.

Then we put that into the equation for the volume of a hempshiere, which again is the volumn of half a sphere
\[ A_{sphere} = \frac{4}{3}\pi r^3\]
\[ A_{hemisphere} = \frac{2}{3}\pi r^3\]


Do you need help solving for a variable and plugging it back in?