Question

in terms of pi, what is the volume of cylinder c? using the volume of cylinder c, what is the height of cylinder d? cylinder c: d = 8 cm, h = 9 cm. cylinder d: d = 4 cm, h (unknown).

Explanation:

Step1: Find the radius of cylinder C

The diameter of cylinder C, $d = 8$ cm, so the radius $r_{C}=\frac{d}{2}=\frac{8}{2}=4$ cm.

Step2: Calculate the volume of cylinder C

The volume formula for a cylinder is $V=\pi r^{2}h$. For cylinder C with $r = 4$ cm and $h = 9$ cm, we have $V_{C}=\pi\times4^{2}\times9=\pi\times16\times9 = 144\pi$ $cm^{3}$.

Step3: Find the radius of cylinder D

The diameter of cylinder D, $d = 4$ cm, so the radius $r_{D}=\frac{d}{2}=\frac{4}{2}=2$ cm.

Step4: Calculate the height of cylinder D

Since $V_{C}=V_{D}$, and $V_{D}=\pi r_{D}^{2}h_{D}$, we can set up the equation $144\pi=\pi\times2^{2}\times h_{D}$. Divide both sides of the equation by $\pi$: $144 = 4h_{D}$. Then solve for $h_{D}$: $h_{D}=\frac{144}{4}=36$ cm.

Answer:

The volume of cylinder C is $144\pi$ $cm^{3}$ and the height of cylinder D is 36 cm.