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Question
The ratio between the curved surface area and the total surface area of a cylinder is 1: 2. Find the ratio between the height and the radius of the cylinder.
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Solution
Let r be the radius and h be the height of a right circular cylinder, then Curved surface area = 2πrh
and total surface area = 2πrh x 2πr2 = 2πr(h + r)
But their ratio is 1: 2
`therefore (2pirh)/(2pir(h + r)) = 1/2`
⇒ `h/(h + r) = 1/2`
⇒ 2h = h + r
⇒ 2h - h = r
⇒ h = r = 1 : 1
Hence, their radius and height are equal.
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