Question

Find the radius of the sphere with a volume of 32/81π cubic yards. Write your answer as a fraction in simplest form.

Answer 1

Explanation:

The formula for the volume of a sphere of radius r is V = (4/3)(π)r^3.

Here we know the volume is V = (32/81)πr^3, but want to find the radius.

V

Solving the above formula for r^3, we get -----------------

(4/3)(π)

32(π)

and so, with V = (4/3)(π)r^3, r^3 = ----------

81

The radius of the sphere is the cube root of the above equation:

r = ∛ [(32(π) / 81 ]

Answer 2

2/3 yards or 2 feet

Explanation:

The formula for the volume of a sphere is
`(4)/(3)\pi r^3`, meaning that you can set up the following equation:

`(32\pi)/(81)=(4)/(3)\pi r^3`

Divide both sides by
`(4)/(3)\pi`:

`(8)/(27)=r^3`

Take the cube root of both sides:

`r=(2)/(3)` yards. Hope this helps!