+1248 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 $144 \pi.$ What is the total surface area of the cylinder?
+129771 Call the radius of the sphere = r = the radius of the cylinder
Call the height of the cylinder = 2r = h
Volume of cylinder = (4/3) pi r^3
144 pi = (4/3) pi r^3
(3/4) 144 = r^3
108 = r^3
(27 * 4) = r^3
3(4)^(!/3) = r
Surface area of cylinder = 2 pi r^2 + 2pi r * h =
2 pi [ 3(4)^(1/3)]^2 + 2 pi [( 3 )(4)^(1/3)] * [(2) (3)(4)^(1/3) ] ≈ 427.48
