Question

A cone, A hemisphere and Acyinder have equal
Radii of there bases and equal heights. Then
Find the ratio of there vaules​

Answer 1

Answer:

1

What is the ratio of their volumes if a cone, a hemisphere, and a cylinder have equal radii of their bases and equal heights?

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Janak Arora

Answered October 6, 2019

The height of a hemisphere = the radius of its base,

say, r.

Since the heights of the cylinder, the cone and the hemisphere are the same as per the conditions of the question,

the height of cylinder= the height of the cone = r

Now, the volume of a right circular cone is given by π/3*r^2*h, where r is the radius of the base of the cone and h is its height. In the present case, h = r.

So, the volume of the cone = π/3*r^2*r = π/3 r^3….(1)

Volume of a hemisphere = 2/3 πr^3 ….(2)

Volume of a cylinder is given by πr^2*h, where r is the radius of its base and h is its height. In the present case, h= r.

So, the volume of the cylinder = πr^2*r = πr^3 ….(3)

The ratio between (1), (2) and (3) is:

1/3 πr^3 : 2/3πr^3 : πr^3

i.e. 1/3 : 2/3 : 1 or,

1 : 2 : 3

So, the ratio between the volumes of a cone, a hemisphere and a cylinder having the same radius of base and the same height will be :

1 : 2 : 3

Hope it helps you..