Question

Two metal spheres (one with radius x cm and the other with radius x+2 cm) will be melted together to create a new single sphere. Express the radius, R, of the new sphere as a function of x.

Answer 1

The volume of the new sphere will be the sum of the volume of the two original spheres.

Volume of sphere with radius x:

V = [4 / 3] π (x^3)

Volume of the spher with radius [4/3] π (x +2)^3

Volume of the new sphere =

[4/3]πR^3 = [4/3]πx^3 + [/3]π(x+2)^3

R^3 = x^3 + (x+2)^3 = x^3 + x^3 + 3(x^2)(2) + 3x(2^2) + 2^3

R^3 = 2x^3 + 6x^2 + 12x + 8

Answer: R^3 = 2x^3 + 6x^2 + 12x + 8