Question

An Iron sphere of radius 'a' unit is immersed completely in water contained In a right circular cone of semi vertical angle 30, water is drained off from the cone

til its surface touches the sphere. Find the volume of water remaining in the cone.​

Answer 1

Answer:

5πa³/3

Step-by-step explanation:

Let R and H be the radius and height of the cone .

In ΔBOC

tan 30° = BC/AC

1/√3 = R / H

H =R √3

In ΔOPD

sin 30° = PD/ OP

1/2 = a/H-a

H -a = 2a

H = 3a

Put H value

√3 R = 3a

H = 3a

R = √3 a

Volume of Cone = 1/3 π R² H = 3πa³

Volume of sphere = 4/3 πa³

Volume of water remaining in the cone = 3πa³-4/3 πa³

= 5/3πa³

To keep