Question

If the volume of a sphere inscribed in a cubic box is 36pi, find the surface area of the box

Answer 1

Surface area of the cube = 216 square units

Explanation:

Let the length of a side of a cube = x unit

Diameter of the sphere inscribed in this cube = length of a side of the cube

Volume of the sphere =
`(4)/(3)\pi r^(3)`

Where r = radius of the sphere =
`(x)/(2)` units

36π =
`(4)/(3)\pi ((x)/(2))^(3)`

36π =
`(4x^(3)\pi )/(24)`

36×24 = 4x³

x =
`\sqrt[3]{(36* 24)/(4) }`

x = 6 units

Length of a side of the cube = 6 units

Surface area of the cube = 6×(Side)²

= 6×(6)²

= 216

= 216 square units