Question

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and
cylinder equal their diameters. Then their volumes are proportional, respectively to
(a) 1 : 3 : 1
(b) 2 : 1 : 3
(c) 3 : 2 : 1
(d) 1 : 2 : 3

Answer 1

My answer is not in the question....
I don't know why...
It is right or not??.. comment

Answer 2

Answer:

The volumes are proportional, respectively to option (a) 1 : 3 : 1

Step-by-step explanation:

Given

Radius of cone = radius of cylinder = radius of hemisphere = r

Height of cone = height of cylinder = h = 2r

Volume of cone = 1/3 x πr²h = 2πr³/3

volume of cylinder = πr²h = 2πr³

Volume of hemisphere = 2πr³/3

Hence the ratio of their volume

= 2πr³/3 :2πr³ :  2πr³/3

= 2/3 : 2 : 2/3

multiplying 3 and dividing 2

= 1 : 3 : 1

Hence the volumes are proportional, respectively to (a) 1 : 3 : 1