Question

an iron sphere of radius a unit is immersed completly in water contained in a right circular cone of semi-vertical angle 30 water is drained off from the cone till 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  =

                         Volume of cone - volume of sphere

=  3πa³  -4/3π a³

= 5/3 πa³