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Question
The difference between the outer and inner curved surface area of a hollow cylinder is 264 cm2. If its height is 14 cm and the volume of the material in it is 1980 cm3, find its total surface area.
Solution
Curved surface area of cylinder = πr2h
Height h = 14cm
The difference between the outer and inner curved surface area = 264cm2
2π x {(Router)-(Rin)} x h = 264cm2
⇒ π x {(Router)-(Rin)} x h = 132 ...(1)
Volume of material in cylinder = 1980cm3
π{(Router)2-(Rin)2} x h = 1980
π{(Rouer)-(Rin){(Router+(Rin)} x h = 1980 ...(2)
Substituting (1) in (2), we get
{(Router+(Rin)} x 132 = 1980
∴ {(Router+Rin)} = 15cm
Total surface area of a hollow cylinder
= 2π{(Router+Rin)} x h + 2π{(Router)2-(Rin)2}
= `2pi xx 15 xx 14 + 2 xx (1980)/(14)`
= 1602cm2
∴ The total surface area of the hollow cylinder is 1602cm2.
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