Question

The radius of a solid sphere and a solid right circular cone are equal and the height of the cone is equal to the
diameter of its base. They are melted and the combined matter is recast into a solid hemisphere. What is the
ratio of the radius of the hemisphere to that of the cone?​

Answer 1

Answer:

ANSWER

Let h be the height of each cone.

Then sum of the volumes of two cones = Volume of the spheres

⇒

3

1

πr

1

2

h+

3

1

πr

2

2

h=

3

4

πR

3

⇒ (r

1

2

+r

2

2

)h=4R

3

⇒h=

(r

1

2

+r

2

2

)

4R

3

[Hence proved]