gauravsoni wrote:
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.
The difference is that B says "\(\frac{60}{\pi}\)", while D says: "\(60\pi\)". Formatted the original post to make it clearer.
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?A. The volume of the cylinder with height 10 is \(\frac{60}{\pi}\) cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is \(\frac{60}{\pi}\) cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is \(60\pi\) cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is \(60\pi\) cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is \(\frac{240}{\pi}\) cubic inches greater than the volume of the cylinder with height 10.
We can make 2 cylinders:
With height of 6 and the radius of the base of \(r=\frac{5}{\pi}\) (from \(2\pi{r}=10\) --> \(r=\frac{5}{\pi}\)) --> \(volume=\pi{r^2}h=\frac{150}{\pi}\).
With height of 10 and the radius of the base of \(r=\frac{3}{\pi}\) (from \(2\pi{r}=6\) --> \(r=\frac{3}{\pi}\)) --> \(volume=\pi{r^2}h=\frac{90}{\pi}\).
The volume of the first one is \(\frac{60}{\pi}\) cubic inches greater than the volume of the second one.
Answer: B.
Thanks Bunuel, I thought of using the width of the rectangle as the radius, now i see that its actually the circumference of the circular base. Thanks for the clarification.