Question: The volumes of a cylinder and a cone are in the ratio 3: 1. Find their diameters and then compare them when their heights are equal.
Options:
A) Diameter of cylinder = Diameter of cone
B) Diameter of cylinder > Diameter of cone
C) Diameter of cylinder < Diameter of cone
D) Diameter of cylinder = 2 times of diameter
Show Answer
Answer:
Correct Answer: A
Solution:
- Let radii of cylinder and cone be $ r _1 $ and $ r _2 $ respectively.
Then, $ \frac{\pi r_1^{2}h}{\frac{1}{3}\pi r_2^{2}h}=\frac{3}{1} $
$ \Rightarrow $ $ \frac{3r_1^{2}}{r_2^{2}}=\frac{3}{1} $
$ \Rightarrow $ $ r _1=r _2 $
$ d _1=d _2 $