A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 ft.
h
Which equation gives the volume of the sphere?

Step-by-step explanation:  

Information we have:

Volume of the cylinder:

The formula for volume of a cylinder is:

where is the radius and and h is the height

and the formula for the volume of a sphere is:

we dont have the height of the sphere in the formula but the height is double the radius:

thus we manipulate the formula for the volume to get a 2r and the substitute with h:

and we substitute that

the value must be equal for the sphere and for the cylinder.

We clear from the volume of the cylinder

and we do the same for the volume of the sphere:

and we equal these two values for  since we are told the radius and the height are the same:

and finally, we clear for the volume of the sphere:

this is the general expression.

and considering the volume of the cylinder is 11ft:

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