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

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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

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