a spherical ball of radius 1 cm is dropped into a conical vessel of radius 3 cm and slant height 6 cm .the volume of water that can just immerse the ball is
Answers
Answered by
2
Given, AB = 3 cm, BC = 6 cm and OF = 1 cm
Height of the cone (AC) = root (6^2 - 3^2) = 3*root (3)
Triangles ABC and CFO are similar (RHS similarity)
So, OC/BC = OF/AB
OC = 2 cm, therefore CG = 3 cm (OG = 1 cm)
Now,
The ABC and CEG both are similar
So, CG/AC = GE/AB
So, GE = root (3)
Required volume = Volume of cone (CDE) - Volume of Sphere
= 3*pi - 4/3*pi
= 5/3*pi
Height of the cone (AC) = root (6^2 - 3^2) = 3*root (3)
Triangles ABC and CFO are similar (RHS similarity)
So, OC/BC = OF/AB
OC = 2 cm, therefore CG = 3 cm (OG = 1 cm)
Now,
The ABC and CEG both are similar
So, CG/AC = GE/AB
So, GE = root (3)
Required volume = Volume of cone (CDE) - Volume of Sphere
= 3*pi - 4/3*pi
= 5/3*pi
Similar questions