The volume of a cylinder is 60 cubic centimeters. The radius of the cylinder is 2. What is the number of cubic centimeters in the volume of the sphere that circumscribes the cylinder?
+128474 We can find the height of the cylinder as follows
60 = pi * 2^2 * height
15 / pi = height
Now.....the radius of the sphere can be found by the Pythagorean Theorem
We have a right triangle with one leg = the radius of the cylinder = 2 and the other = (1/2) the height of the cylinder = 7.5 / pi
The radius of the sphere is the hypotenuse of this triangle = sqrt [ 2^2 + (7.5/pi)^2 ] =
sqrt [ 4 + 56.25/pi^2 ] = [ 4 + 56.25 / pi^2]^(1/2)
The volume of this sphere = (4/3) pi * [ 4 + 56.25/pi^2] ^(3/2) ≈ 126.5 cm^3
