Question

1. which cylinder has twice the volume of the cylinder shown below? (adapted from 1992 amc 8 problem, question #16) a. b. c. d. e. none of the above

Explanation:

Step1: Recall volume formula for cylinder

The volume formula of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height. Let's assume the original - cylinder has radius $r$ and height $h$.

Step2: Calculate volume of each option

For option A: $r = 20$, $h = 5$, so $V_A=\pi\times20^{2}\times5=\pi\times400\times5 = 2000\pi$.
For option B: $r = 10$, $h = 10$, so $V_B=\pi\times10^{2}\times10=\pi\times100\times10 = 1000\pi$.
For option C: $r = 5$, $h = 20$, so $V_C=\pi\times5^{2}\times20=\pi\times25\times20 = 500\pi$.
For option D: $r = 20$, $h = 10$, so $V_D=\pi\times20^{2}\times10=\pi\times400\times10 = 4000\pi$.
Let's assume the original cylinder has $r = 10$ and $h = 10$, then its volume $V=\pi\times10^{2}\times10 = 1000\pi$. The cylinder with twice the volume has $V = 2000\pi$.

Answer:

A. A cylinder with radius 20 and height 5