A solid right circular cone of base diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.
C
Correct answer
Explanation
Radius of base of cone is 7 cm and height is 8 cm.
Volume of cone = 1/3 $\pi$ r2 h = 1/3$\pi$ (7)2 x 8 cm3
External radius of hollow sphere = 5 cm
Let internal radius be r cm.
Volume of hollow sphere = 4/3 $\pi$ (R3 - r3) cm3 = 4/3 $\pi$ (53 - r3) cm3
Since volume of material used for cone will be the same as the volume of material used to make hollow sphere,
1/3 $\pi$ (7)2 8 = 4/3 $\pi$ (125 - r3) $\Rightarrow$ 98 = 125 - r 3
r3 = 125 - 98 = 27
r = 3 cm
So, internal diameter of the sphere will be 2r = 2 x 3 = 6 cm.