Question

The volume of a right circular cylinder is 12π in cubed. express the height as a function of the radius. Express the total surface area as a function of the radius.

Answer 1

Ok, so we know
\[
\text{cylinder_height} = h \\
v = \text{base_area} \cdot h = 12 \pi \\
\text{base_area} = \pi \cdot r^2 \\
f(r) =h = \frac{ \text{base_area} \cdot h }{\text{base_area}} = \frac{v}{\text{base_area}} = \frac{12\pi}{\pi \cdot r^2} = \frac{12}{r^2} \\
g(r) = \text{surface} = \text{base_circumference} \cdot h = 2 \pi r \cdot \frac{12}{r^2} = \frac{24 \pi}{r}
\]