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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 338 p `cm^2`. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.
Solution
Given that,
External radius(R) =8cm
Height (h)= 10cm
The total surface area of a hollow metal cylinder = 338 IT `cm^2`
We know that
`2 πRh + 2πrh + 2πR^2 - 2πR^2=338πR.`
⇒h(R+r) = (R+r) (R-r)=169
⇒10(8+r)+(8+r)(8-r)=169
⇒80+10r+64-`r^2`=169
⇒`x^2` -10r+25=0
⇒r=5
∴R-r=8-5cm=3cm
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