Question

the base radius of two cones are in the ratio 3 : 4 and their volumes are equal. find the ratio of their Heights?​

Answer 1

Step-by-step explanation:

Given:-

The base radius of two cones are in the ratio 3 : 4

and their volumes are equal.

To find:-

Find the ratio of their Heights?

Solution:-

The ratio of the radius of the base of the two cones = 3:4

Let they be 3X and 4X units

Let the Radius of the first cone = 3X units

Let the radius of the second cone = 4X units

Let the height of the first cone be h1 units

And The height of the second cone be h2 units

Volume of a cone = (1/3)πr^2h cubic units

Volume of the first cone V1

=>(1/3)×π×(3X)^2×h1 cubic units

=>V1 = (1×π×9X^2×h1)/3 cubic units

V1 = 3πX^2h1 cubic units ------------------(1)

Volume of the second cone = V2

=>(1/3)×π×+4X)^2×h2 cubic units

=>V2 = (1×π×16X^2×h2)/3 cubic units

V2 =(16πX^2h2)/3 cubicunits---------------(2)

Given that

Volumes of the two cones are equal.

=>(1)=(2)

=>V1 = V2

=>3πX^2h1 = ( 16πX^2h2 ) /3

=>3(3πX^2 h1) = 16 πX^2 h2

=>9πX^2 h1) = 16 πX^2 h2

On cancelling πX^2 both sides then

=>9 h1 = 16 h2

=>9h1/h2 = 16

=>h1/h2 = 16/9

=>h1 : h2 = 16:9

Ratio of their Heights = 16:9

Answer:-

The ratio of the heights of the two cones = 16:9

Used formulae:-

• Volume of a cone = (1/3)πr^2h cubic units

Where 'r' is the radius and 'h' is the height and π=22/7