Question

A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. find the diameter of the base of the cone.​

Answer 1

$\huge\rm\underline\red{Answer✿࿐}⠀$

It is given that

Diameter of the sphere =15.6 cm

Radius of the sphere =

2

15.6

=7.8 cm

Height of the cone =31.2 cm

We know that

3

4

πR

3

=

3

1

πr

2

h

So we get

3

4

×

7

22

×7.8

3

=

3

1

×

7

22

×r

2

×31.2

On further calculation

r

2

=

3

1

×

7

22

×31.2

3

4

×

7

22

×7.8

3

So we get

r

2

=

31.2

(4×474.552)

=60.84

By taking square root on the RHS

r=7.8cm

Diameter =2(7.8)=15.6cm

Therefore, the diameter of the base of the cone is 15.6 cm.