A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar. The volume of the cylinder is 432pi

Question

What is the volume of the sphere?

I have a particularly had time with the higher geometry, so a thorough explanation would be great!

Answer 1

the height of the cylinder is equal to the diameter of the sphere

the diameter is twice the radius, or d=2r

V=∏r^2h is the formula for the volume of a cylinder

the volume of the cylinder is 432∏ and the height of the cylinder is h=2r

substitute

432∏=∏*r^2*2r

432∏=∏*r^3*2

divide both sides by 2∏

216=r^3 (r=6 by the way but we don't need to know this)

V=(4/3)∏r^3 is the formula for the volume of a sphere

V=(4/3)∏(216) (remember that r^3=216)

simplify

V=4*∏*72

V=288∏ is the volume of the sphere