Question

A cone and a cylinder have the same height and their bases are congruent circles

If the volume of the cylinder is 90 cm^3,
what is the volume of the cone?

Answer 1

Answer:

30 cm^3

Step-by-step explanation:

Given

radius for both shape = r

height  for both shape = h

volume of cylinder is given by $\pi r^2h$

volume of cone is given by $1/3(\pi r^2h)$

From above two equation we can see that  $\pi r^2h$ is volume of cylinder

thus we can say that volume of cone is 1/3(volume of cylinder)

So we can say that for any cylinder and cone whose height is same and base is congruent

volume of cone will be one-third of volume of cylinder.

Now in given problem

volume of cylinder is 90 cm^3

So , volume of given cone will be one-third of 90 cm^3

which is 1/3*90 cm^3 = 30 cm^3.

Thus, volume of the given cone is 30 cm^3.

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