Question

A cone and sphere have the same radius of 12 cm. find the height of the cone if the cone and sphere have the same volume.

Answer 1

Given:

Radius of cone(r) = radius of sphere(r)= 12 cm

Volume of cone = volume of sphere

1/3 × π × r²h = 4/3πr³

12² × h = 4× 12³

h=( 4 × 12³)/ 12²

h= 4× 12

h = 48 cm.

Hence, the height of the cone is = 48 cm.

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Hope this will help you.....

Answer 2

Solution :-

As mentioned in the question that the radius of the cone and the radius of the sphere is same.

So,

Radius of the cone = Radius of the sphere = 12 cm

Also given that the volume of the cone and the volume of the sphere is same.

Volume of the cone = 1/3*πr²h 

Volume of the sphere = 4/3πr³

⇒ Volume of cone = Volume of sphere

⇒ 1/3πr²h = 4/3πr³

1/3*π*12²*h = 4/3*π*12³

⇒ (144/3)*h = 6912/3

⇒ 48h = 2304

⇒ h = 2304/48

⇒ h = 48 cm

Hence, the height of the cone is 48 cm.

Answer.