a storage bin is shaped like a cylinder with a hemisphere shaped top. the cylinder is 45 inches tall. the volume of the bin is 4131 pi cubic inches. find the radius of the bin.

Question

i think [4(pi)r(cubed)]/3=volume of hemisphere

and h (pi) r squared volume of the cylinder.

so

[4(pi) r (cubed)/3] + [45 (pi) r squared= volume of bin

so

[4 r (cubed)/3] + [45 (pi) r squared=volume

how do i solve for r?

sorry, i'm stuck

Answer 1

the volume of a sphere is 4/3 PI r^3, so a hemisphere would be half of that.

If you have an equation such as this,

a r^3 + b r^2 + c=0

it is a third degree equation. I think I would graph
f(r)= a r^3+b r^2+c and see where it crosses the axis, that is a solution.
There are ways to solve cubic equations, but for this, I would graph it.

Answer 2

thanks Mr. Pursley,
graphing it now.