The cylinders are similar the volume of the larger cylinder is 1600 cubic centimeters what is the volume of the smaller cylinder

We are given Volume of the larger cylinder is = 1600 cubic centimeters.

Height of the larger cylinder = 16 cm.

We know formula of volume of a cylinder V=, where r is the radius of cylinder,  h is the height of the cylinder.

Plugging value of V and h of larger cylinder, we get

Dividing both sides by 16, we get

Taking square root on both sides, we get

r=10.

Therefore, radius of the larger cylinder is 10 cm.

We are given cylinders are similar .

Note: The radii and heights of similiar cylinders are in same ratio.

Therefore, we can setup a proportion:

Let us take radius of small cylinder is x.

Multiplying both sides by 10, we get

x=2.50.

Therefore, radius of the small cylinder = 2.5 cm.

Now, plugging radius =2.5 and height  = 4 in the formula of volume the cylinder, we get

Therefore, correct option is 25 pi cm^3.

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