Question

a cone and a cylinder are having equal base radius .Find the ratio of the heights of cone and cylinder if their volumes are equal .

Answer 1

$We \: know \: that,$

Volume of Cone = 1/3πr²h.
Also, Volume of cylinder = πr²h.

As, the bases are equal, Radius of cone = Radius of cylinder = r.

Also, the volumes are equal.
Let the height of cone be a and height of cylinder be b.

Now, 1/3π(r²)a = πr²b

1/3a = b

a = 3b

a/b = 3/1 .

Therefore, Ratio of heights of cone and cylinder = 3 : 1

Answer 2

Answer:

Weknowthat,

Volume of Cone = 1/3πr²h.

Also, Volume of cylinder = πr²h.

As, the bases are equal, Radius of cone = Radius of cylinder = r.

Also, the volumes are equal.

Let the height of cone be a and height of cylinder be b.

Now, 1/3π(r²)a = πr²b

1/3a = b

a = 3b

a/b = 3/1 .

Therefore, Ratio of heights of cone and cylinder = 3 : 1