Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm .It is melted and recast into a sphere.Then, what will be the radius of the sphere?

Answer 1

Radius of cone = 2.1 cm.
Height of cone = 8.4 cm.
Let the radius of sphere be R cm.
Now,
Volume of sphere = Volume of cone
=> 4/3 * pi * R^3 = 1/3 * pi * r^2 * h
=> 4*R^3 = r^2*h
=> R^3 = 2.1*2.1*8.4/4
=> R^3 = 37.044/4
=> R = cube root 9.261
=> R = 2.1 cm.

Answer 2

Since volume of sphere = volume of cone
4/3 pi r^3 = 1/3 pi R^2 h
4 r^3 = (2.1)^2 × 8.4
r^3 = (2.1)^2 × 2.1
r^3 = (2.1)^3
So r= 2.1 cm
so radius of sphere is r is 2.1 cm