Question

cylinder c and d have the same volume. round to the nearest hundredth if necessary. 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 = 5 cm. cylinder d: d = 6 cm, h cm.

Explanation:

Step1: Find 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 volume of cylinder C

The volume formula for a cylinder is $V=\pi r^{2}h$. For cylinder C with $r = 4$ cm and $h = 5$ cm, $V_{C}=\pi\times4^{2}\times5=\pi\times16\times5 = 80\pi$ $cm^{3}$.

Step3: Find radius of cylinder D

The diameter of cylinder D, $d = 6$ cm, so the radius $r_{D}=\frac{d}{2}=\frac{6}{2}=3$ cm.

Step4: Calculate height of cylinder D

Since $V_{C}=V_{D}$, and $V_{D}=\pi r_{D}^{2}h_{D}$, we have $80\pi=\pi\times3^{2}\times h_{D}$. Canceling out $\pi$ on both sides gives $80 = 9h_{D}$. Then $h_{D}=\frac{80}{9}\approx8.89$ cm.

Answer:

$8.89$ cm