the ratio of total surface area to the curved surface area of a right circular cylinder is 3:2 find the volume if its total surface area is 14784 cm2

Answer 1

total SA = 2πr^2 + 2πrh ---> top + bottom + side
curved SA = 2πrh

(2πr^2 + 2πrh)/2πrh = 3/2
4πr^2 + 4πrh = 6πrh
4πr^2 = 2πrh
divide by 2πr
2r = h

2πr^2 + 2πrh = 14784
2πr^2 + 2πr(2r) = 14784
6πr^2 = 14784
r^2 = 2464/π
r = appr 28.01 cm
h = appr 56.01 cm