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

\[ (1)\ A_{hemisphere} = 2\pi r^2\]
\[(1)\ V_{hemisphere} = \frac{2}{3}\pi r^3\]

We use 1 to find r

\[ 243\pi ft^2 = 2\pi r^2\]
\[ 121.5 ft^2 = r^2 \ (divide\ by\ 2 \pi)\]
\[ 11.0 ft = r \ (square root)\]

So now that we have r, we plug it back into our volume equation:

\[ V_{hemisphere} = \frac{2}{3}\pi r^3\]
\[ V_{hemisphere} = \frac{2}{3}\pi (11.0ft)^3\]
\[ V_{hemisphere} = \frac{2}{3}\pi \cdot 1331ft^3 \]
\[ V_{hemisphere} = 887\pi ft^3 \]

Answer 2

Thank you sooo much!!

Answer 3

u knew it was a half circle with a line going to the middle right?

Answer 4

A hemisphere is half a sphere, which is a 3D object. A semicircle is a 2D object.
I assumed it was this:
http://www.k6-geometric-shapes.com/image-files/hemisphere.jpg

Answer 5

yea exactly! thank you!!