Question

The volume of a sphere can be determined by the formula V = 4/3 πr^3, where r is the radius. What is the volume of a sphere with radius 3/2x^3y^–2 in terms of x and y?

Answer 1

`V = (99)/(7) x^(9)y^(-6)`

Explanation:

Given

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

Required

Find V when

`r = (3)/(2)x^3y^{-2`

Substitute
`(3)/(2)x^3y^{-2` for r in
`V = (4)/(3)\pi r^3`

`V = (4)/(3)\pi * ((3)/(2)x^3y^(-2))^3`

Open bracket

`V = (4)/(3)\pi * (3)/(2)^3 * x^(3*3)y^(-2*3)`

`V = (4)/(3)\pi * (27)/(8) * x^(9)y^(-6)`

Simplify the fractions

`V = \pi * (9)/(2) * x^(9)y^(-6)`

Let

`\pi = (22)/(7)`

So:

`V = (22)/(7) * (9)/(2) * x^(9)y^(-6)`

`V = (11)/(7) * (9)/(1) * x^(9)y^(-6)`

`V = (99)/(7) * x^(9)y^(-6)`

`V = (99)/(7) x^(9)y^(-6)`