Question

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Answer 1

In the given problem, we have a hollow sphere of given dimensions;

Internal diameter of the sphere (d) = 4 cm

External diameter of the sphere (D) = 8 cm

Now, the given sphere is molded into a cone,

Diameter of the base of cone (d_c) = 8 cm

Now, the volume of hollow sphere is equal to the volume of the cone.

So, let the height of cone = h cm

Therefore, we get

Volume of cone = the volume of hollow sphere

`(1/3) pi ((d_c)/2)^2 h = (4/3) pi ((D/2)^3 -(d/2)^3)`

`(1/3) pi (8/2)^2 (h) = (4/3) pi ((8/2)^3 -(4/2)^3)`

`(1/3)pi (4)^2 (h) = (4/3) pi (64-8)`

Further, solving for h,

` h = ((4/3) pi (56))/((1/3) pi (16))`

`h = ((4)(56))/((16))`

h = 14 cm

So, height of the cone is 14 cm