The ratio of the base radii of a cylinder and a cone is 3 : 4 and their heights are in the ratio 2 : 3. Then the ratio of their volume:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 : 8
The volume of a cylinder is \(\pi r^2h\) and that of a cone is \(\frac{1}{3}\pi r^2h\). With radii in the ratio 3 : 4 and heights in the ratio 2 : 3, the radii can be taken as \(3k\) and \(4k\) and the heights as \(2m\) and \(3m\); the cone’s factor \(\frac{1}{3}\) must not be left out.
Volume of the cylinder: \(\pi(3k)^2(2m)=18\pi k^2m\)
Volume of the cone: \(\displaystyle \frac{1}{3}\pi(4k)^2(3m)=16\pi k^2m\)
Ratio of the volumes, \(\pi k^2m\) cancelling: \(18:16=9:8\)