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The total surface area of a hollow cylinder open at both ends of external radius 8cm and height 10cm is 338pie cm^2. Taking r

to be inner radius, find thickness of the metal in the cylinder.



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Let the outer radius be R 
and inner radius be r
total surface area = inner surface area + outer surface area +2(area of                                            thickness)
                             = 2πrh + 2πRh + 2π(R² -r²)
⇒338π = 20πr + 160π + 128π - 2πr²
⇒2πr² - 20πr + 50π =0
⇒r² -10r + 25 =0
⇒(r -5)²=0
⇒r =5 cm
so thickness of the metal in cylinder = R- r = 8- 5 = 3 cm

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