Question

The volume of a cylinder is 1296π cm^3 and it's height is 16 cm.The length of the cylinder's radius is ___ cm.

Answer 1

Recall that the volume of a cylinder is given by

$V=\pi\cdot r^2\cdot h$

Where r is the radius and h is the height of the cylinder.

For the given case, we are given

V = 1296π cm³

h = 16 cm

Let us substitute these values into the above formula and solve for the radius

$\begin{gathered} V=\pi\cdot r^2\cdot h \\ 1296\pi=\pi\cdot r^2\cdot16 \\ \frac{1296\pi}{16\pi}=r^2 \\ \frac{1296}{16}=r^2 \\ 81=r^2 \\ \sqrt{81}=r \\ 9=r \\ r=9\: cm \end{gathered}$

Therefore, the length of the cylinder's radius is 9 cm