Question

the bases of cylinder a and cylinder b are circles with the same radius. the volume of cylinder a is 100π cubic centimeters. what is the volume of cylinder b? write an exact answer in terms of π.

Explanation:

Step1: Find the radius of cylinder A

The volume formula for a cylinder is $V = \pi r^{2}h$. Given $V_A=100\pi$ and $h_A = 4$. Substitute into the formula: $100\pi=\pi r^{2}\times4$. Divide both sides by $4\pi$ to get $r^{2}=25$, so $r = 5$ cm.

Step2: Calculate the volume of cylinder B

Cylinder B has the same - radius $r = 5$ cm and height $h_B=3$ cm. Using the volume formula $V=\pi r^{2}h$, substitute $r = 5$ and $h = 3$: $V_B=\pi\times5^{2}\times3$.
$V_B=\pi\times25\times3=75\pi$ cubic centimeters.

Answer:

$75\pi$ cubic centimeters