The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 200pi.
+128474 We have that
200pi = pi ( 5h/6)^2 * h divide out pi
200 = (25/36) h^2 * h nutiply both sides by 36/25
288 = h^3 take the cube root of both sides
( 288)^(1/3) = h = (6* 2 * 6 * 2 * 2)^(1/3) = 2*(36)^(1/3)
And the radius is (5/6)* 2*(36)^(1/3) = (5/3)* (36)^(1/3)
Surface area = 2*pi * r^2 + 2 *pi * r * h =
2pi [ r^2 + r * h ] =
2pi [ (25/9)* (36)^(2/3) + (10/3) * (36)^(2/3) ] ≈ 418.6 units^2
