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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.
Solution
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.
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