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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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Respuesta :

calculista

Answer:

Part 1) The volume of the cylinder is [tex]V=108\ units^{3}[/tex]

part 2) The volume of the sphere is [tex]V=144\ units^{3}[/tex]

Step-by-step explanation:

step 1

Find the radius of the cone

we know that

the volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=36\ units^{3}[/tex]

[tex]h=r\ units[/tex]

substitute and solve for r

[tex]36=\frac{1}{3}\pi r^{2} (r)[/tex]

[tex]108=\pi r^{3}[/tex]

[tex]r^{3}=108/ \pi[/tex] ------> equation A

step 2

Find the volume of the cylinder

we know that

the volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=r\ units[/tex]

substitute

[tex]V=\pi r^{2} (r)[/tex]

[tex]V=\pi r^{3}\ units^{3}[/tex]

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\pi (108/ \pi)\ units^{3}[/tex]

[tex]V=108\ units^{3}[/tex]

step 3

Find the volume of the sphere

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}\ units^{3}[/tex]

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\frac{4}{3}\pi (108/ \pi)[/tex]

[tex]V=144\ units^{3}[/tex]

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