UPSC CDS Math Volume and Surface Area Questions

Let r and h be the radius and height of the cone, respectively. In ΔCOD and ΔOAB
∠COD = ∠AOB (Common)
∠OCD = ∠OAB (90° each)
∴ ΔOCD ≈ ΔOAB (AA similarity)
⇒

CD

AB

=

OC

OA

(Corresponding sides are proportional)
⇒

r

AB

=

h

h 2

⇒AB=

r

2

Therefore, volume of water
=

1

3

π(AB)2×OA=

1

3

π(

r

2

)2×

h

2

=

1

8

×

1

3

πr2h=

V

8