Question

(x) The diameter of one sphere is double the diameter of another sphere. If
the numerical value of total surface area of larger sphere is equal to the
volume of smaller sphere, then find the radius of the smaller sphere,​

Answer 1

Answer:

6 units

As given in the question, the diameter of larger sphere is double the diameter of smaller sphere. This implies that the radius of larger sphere is the double of the radius of smaller sphere.

So let's assume the radius of smaller sphere to be r, then radius of larger sphere is 2r.

Given: magnitude wise:-

total surface area of larger sphere = volume of smaller sphere

2(pi)[(2r)^2] = [4(pi)(r^3)/3

So on solving this equation we get that r=6 satisfies this equation which apparently is the value of radius of small sphere.