Question : A cone and a cylinder have the same height and the radius of the cone is twice of the radius of the cylinder: What is the ratio of the volume of the cone to that of the cylinder?
Option 1: 2 : 5
Option 2: 4 : 5
Option 3: 3 : 2
Option 4: 4 : 3
Correct Answer: 4 : 3
Solution :
Given: Height $(h)$ = same for cylinder and cone
Let the radius of the cylinder be $r$
Radius of cone = $2r$
Volume of a Cone = $\frac{1}{3}\times\pi \times r^2\times h$
= $\frac{1}{3}\times\pi \times 4r^2\times h$
Volume of a Cylinder = $\pi \times r^2\times h$
The ratio of the volume of the cone to the volume of the cylinder
$=\frac{1}{3}\times\pi \times 4r^2\times h:\pi \times r^2\times h$
$= 4 : 3$
Hence, the correct answer is 4 : 3.
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