# Question #606dc

May 25, 2017

The volume of the cylinder is $108$ cubic units and the volume of the sphere is $144$ cubic units.

#### Explanation:

The formula for volume of a cone is:

$V c o = \pi {r}^{2} \frac{h}{3}$, where $V c o =$Volume (of cone), $r =$radius, and $h =$height.

Since we know that $h = r$, we can write:

$V c o = \pi {r}^{3} / 3$

Substituting the value for the volume:

$36 = \pi {r}^{3} / 3$

Multiply both sides by $\frac{3}{\pi}$.

$36 \times \frac{3}{\pi} = {r}^{3}$

${r}^{3} = \frac{108}{\pi}$

The formula for volume of a cylinder is:

$V c y = \pi {r}^{2} h$, where $V c y =$Volume (of cylinder), $r =$radius, and $h =$height.

Since we know that $h = r$, we can write:

$V c y = \pi {r}^{3}$

From the first calculation, we know the value of ${r}^{3}$ so we substitute that.

$V c y = \pi \times \frac{108}{\pi}$

$V c y = \cancel{\pi} \times \frac{108}{\cancel{\pi}}$

$V c y = 108$

Hence, the volume of the cylinder is $108$ cubic units.

The formula for volume of a sphere is:

$V s = \frac{4}{3} \pi {r}^{3}$, where $V s =$Volume (of sphere), and $r =$radius.

From the first calculation, we know the value of ${r}^{3}$ so we substitute that.

$V s = \frac{4}{3} \pi \times \frac{108}{\pi}$

$V s = \frac{4}{3} \cancel{\pi} \times \frac{108}{\cancel{\pi}}$

$V s = \frac{4}{3} \times 108$

$V s = \frac{4}{1 \cancel{3}} \times 36 \cancel{108}$

$V s = 4 \times 36$

$V s = 144$

Hence the volume of the sphere is $144$ cubic units.