Management Aptitude Test 2015 Paper

Question : 115 of 200

Marks: +1, -0

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius and the heights of cone and cylinder are equal to their diameters. Then, their volumes are proportional, respectively to

1 : 3 : 1
2 : 1 : 3
3 : 2 : 1
1 : 2 : 3

Validate

Solution:

(a)

Volume of cylinder =

πr^2h

Volume of cone =

1/3πr^2h

Volume of hemisphere =

2/3πr^3

Ratio of their volumes
=

1/3πr^2h

πr^2h

2/3πr^3

⇒

1/3 r^2⋅2r

r^2⋅2r

2/3 r^3

⇒

1/3 r^3

2r^3

2/3 r^3

⇒

2/3:2:2/3

⇒ 2 : 6 : 2
∴ 1 : 3 : 1

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