Question

The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338π cm². Taking r to be inner radius, write down an equation in r and use it to state the thickness of the metal in the cylinder.

Answer 1

Surface area of the hollow cylinder = 338π cm²

2π(8)10 + 2π(r)10 + 2[ π(8)² - π(r)²] = 338 π
⇒ 160 + 20r + 2(64 - r²) = 338
⇒  - 2r² + 20r - 50 = 0
⇒  r² - 10r + 25 = 0
⇒  (r - 5)² = 0
⇒  r = 5

∴ Thickness of the metal in the cylinder = 8 - r = 8 - 5 = 3 cm.