UPSC CDS Math Volume and Surface Area Questions

Let the height of the cone be h units and radius of the cone be r units.
OB = h units and BC = r units
∴AD=

r

2

units
Now,ΔOAD ~ ΔOBC (AA Similarity)
∴

AD

BC

=

OA

OB

⇒OA=h×

r 2

r

=

h

2

units
∴

Volume of frustum of cone

Volume of whole cone

=‌‌

‌‌ 1 3 πr2h−‌‌ 1 3 π(‌‌ r 2 )2‌‌ h 2

1 3 πr2h

=‌‌

1−‌‌ 1 8

1

=

7

8

Thus, the ratio of the volume of the frustum of cone to that of the whole cone is 7 : 8.