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.

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asked Mar 16 in Class X Maths by muskan15 (-3,360 points)

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 metal in the cylinder.

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answered Mar 16 by navnit40 (-4,312 points)

Surface area of the hollow cylinder = 338π, cm2

2π(8)10 + 2π(r)10 + 2[π(8)2 – π(r)2] = 338π

⇒ 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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