Question

A sphere is inscribed in a cube with a volume of 64 cubic inches. What is the volume of the sphere? Round your answer to the nearest whole number.

Answer 1

the volume of the sphere is

`33.51 in^(3)`

Explanation:

This problem bothers on the mensuration of solid shapes, sphere and cube.

Given data

Volume of cube v = 64 cubic inches

since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,

we know that volume of cube is expressed as

`v= l*b*h`

`v=l^(3)`

`64= l^(3)`

`l= \sqrt[3]{64}`

`l= 4 in`

also diameter d=length l

Diameter d=
`4in`

Radius r =
`(d)/(2)`=
`(4)/(2)`=
`{2 in}`

Height h=
`4in`

we know that the volume of a sphere is given by

`v= (4)/(3) \pi r^(3)`

substituting into the formula we have

`v= (4)/(3) \ *3.142*2^(3) \\v=\frac{4*3.142*8}3} \\v= (100.54)/(3) \\v= 33.52in^(3)`