UPSC CDS Math Volume and Surface Area Questions

We have,
External radius of the sphere, r1=3cm[∵ diameter =2× radius ]
Internal radius of the sphere, r2=2cm
Volume of metal in the hollow sphere =‌

4

3

π(r13−r23)
=‌

4

3

π×(33−23)
=‌

76π

3

cm3
Given that radius of the cone formed, R=4cm.
Let the height of the cone be h.
cone =‌

1

3

πR2h
Volume of the
=‌

1

3

π×42×h
=‌

16πh

3

cm3
∴‌ Volume of the cone ‌=‌ volume of metal in the sphere ‌
⇒‌

16πh

3

=‌

76π

3

⇒‌‌h=‌

76

16

=4.75