M4maths Previous Puzzles

13 Jan 2022 Area & Volume

A sphere of radius 3 m is melted to form a cylinder and a cone of equal weights and heights. Find the ratio of radii of cylinder and cone.

OPtion

1) 12√3 : 1
2) √3 : 1
3) 9 : √2
4) 2 : 3
5) 1 : 3
6) 2 : √3
7) 9 : 2
8) 3 : 1
9) 1 : √3
10) None of these

Solution

Volume of Sphere = (4/3)*π*r^3 = (4/3)*π*3^3 = 36π
Given, weight and height of a cylinder & a cone is same
Hence, Volume of cylinder = Volume of cone = Volume of sphere/2 = 18π
Let radius of cylinder=r and cone=R and height=h
Volume of cylinder = π*r^2*h = 18π and
Volume of Cone = (1/3)*π*R^2*h = 18π
Comparing above volumes, we get (r/R)^2=1/3
r/R = 1/√3

Correct Option: 9 Best Solution (0)