Let [tex]r_A, h_A[/tex] be the radius and height of cylinder A, and [tex]r_B, h_B[/tex] be the radius and height of cylinder B.
We know that [tex]h_A=h_B=3[/tex]. 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
[tex]V = \pi r^2 h[/tex]
And we have
[tex]V_A = \pi\cdot 4^2\cdot 3 = 48\pi[/tex]
[tex]V_B = \pi\cdot 6^2\cdot 3 = 108\pi[/tex]
Which means that the volume of cylinder B is 108/48=2.25 times greater than the volume of cylinder A
