Cylinder A and cylinder B have a height of 3 inches, but cylinder B has a diameter four inches greater than that of cylinder A. If the diameter of cylinder B is 12 inches, how m…

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asked Feb 11, 2020 206k views

1 Answer

Rhens · Answer 1 · 2020-02-18T04:06:16+0000

Let
r_A, h_A be the radius and height of cylinder A, and
r_B, h_B be the radius and height of cylinder B.

We know that
h_A=h_B=3 . Since the diameter of cylinder B is 12, its radius is 6.

Since the diameter of cylinder B is 4 inches greater than that of cylinder A, the diameter of cylinder A is 8, which implies that its radius is 4.

The formula for the volume of a cylinder is

$V = \pi r^2 h$

And we have

$V_A = \pi\cdot 4^2\cdot 3 = 48\pi$

$V_B = \pi\cdot 6^2\cdot 3 = 108\pi$

Which means that the volume of cylinder B is 108/48=2.25 times greater than the volume of cylinder A