From statement I, h + r = 24 metre Total surface area of the cylinder = 2πrh + 2πr2 ⇒ 2nr (h + r) = 2112 ⇒ 2 ×
22
7
r × 24 = 2112 ⇒ r =
2112×7
2×22×24
= 14 metres .∴ h = 24 - 14 = 10 metre ∴ Volume of cylinder = πr2h = (
22
7
× 14 × 14 × 10) cu metre = 6160 cu.metre From statement II, Radius = 2x metre and height = 2y metre where x and y are co-primes. ∴ LCM = 2xy = 70 ⇒ xy = 35 = 7x5 ∴ Radius = 2 x 7 = 14 metre Height = 10 metre because 142 - 102 = 196 - 100 = 96