Question

The volume of a cylinder cone and sphere are shown below. The three figures have the same radius. The cylinder and the cone have the same height with h = r.
if the volume of the cone is 36 cubic units, what are the volumes of the cylinder and sphere? Explain your answer.

answers: Cylinder:_______cubic units
sphere:________cubic units
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Answer 1

Answer:

Part 1) The volume of the cylinder is $V=108\ units^{3}$

part 2) The volume of the sphere is $V=144\ units^{3}$

Step-by-step explanation:

step 1

Find the radius of the cone

we know that

the volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$V=36\ units^{3}$

$h=r\ units$

substitute and solve for r

$36=\frac{1}{3}\pi r^{2} (r)$

$108=\pi r^{3}$

$r^{3}=108/ \pi$ ------> equation A

step 2

Find the volume of the cylinder

we know that

the volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$h=r\ units$

substitute

$V=\pi r^{2} (r)$

$V=\pi r^{3}\ units^{3}$

substitute the equation A in the formula above

$r^{3}=108/ \pi$ ----> equation A

$V=\pi (108/ \pi)\ units^{3}$

$V=108\ units^{3}$

step 3

Find the volume of the sphere

we know that

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}\ units^{3}$

substitute the equation A in the formula above

$r^{3}=108/ \pi$ ----> equation A

$V=\frac{4}{3}\pi (108/ \pi)$

$V=144\ units^{3}$