Question

What would the radiusof a hemisphere be if the volume is 140000pi

Answer 1

Answer:
`10\sqrt[3]{210}` units, (about 59.4)

Explanation:

a hemisphere is half a sphere.

the volume of a sphere is
`(4)/(3) \pi r^3`

since we need half of this, the volume of a hemisphere would be:
`(4)/(6) \pi r^3`

this simplified nicely to:
`(2)/(3) \pi r^3`

next, we want to find the radius, given the volume. So lets set up the equation.

`140000\pi = (2)/(3) \pi r^3`

`140000 = (2)/(3) r^3` --- cancel a pi from both sides.

`210000 = r^3` ---- multiply both sides by 3/2 to cancel the 2/3.

`\sqrt[3]{210000 }= r` ---- take the cube root of both sides to find r

`10\sqrt[3]{210} = r`

Thats the exact answer: the radius is
`10\sqrt[3]{210}` units.

a decimal approximation is about 59.4 units.