Question

a cube and a sphere has equal total surface area find the ratio of the volume of Sphere and cube

Answer 1

volume of a cube is edge 3and
you easily find

Answer 2

Answer:

√(6/π).

Step-by-step explanation:

Let's assume the radius of the sphere is 'r' unit and length of a side of the cube is 'a' unit.

Thus, surface area of the sphere = 4πr²

And, the surface area of the cube = 6a²

Given, 4πr² = 6a²

Now, let's assume a factor k = 4πr² = 6a²

Thus, 4πr² = k

or, r² = k/4π

or, r = (√k)/(2√π)

or, r³ = [k^(3/2)] / [8{π^(3/2)}]

or, (4/3)πr³ = [k^(3/2)] / (6√π)

Now, k = 6a²

or, a² = k/6

or, a³ = [k^(3/2)] / [6^(3/2)]

Volume of sphere = (4/3)πr³

Volume of cube = a³

Therefore,

[(4/3)πr³ / a³] = [k^(3/2)] / (6√π) X [6^(3/2)] / [k^(3/2)]

or, [(4/3)πr³ / a³] = 6^(3/2) / 6√π

or, [(4/3)πr³ / a³] = √6 / √π

or, [(4/3)πr³ / a³] = √(6/π)

Thus, the ratio of the volumes of sphere and cube = √(6/π).