Question

A solid sphere of radius r is melted and recast in to the shape of cone of height r find the radius of the base of cone

Answer 1

Answer:

Radius of sphere =r

Volume of sphere =

3

4

πr

3

Let radius of the base of cone be R and height is h=r

Now volume of cone =

3

1

πr

2

h =

3

1

πR

2

r

But Volume of cone = Volume of sphere

⇒

3

1

πR

2

r=

3

4

πr

3

⇒R

2

=4r

2

⇒R=2r

Hence, radius of base of cone =2r