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Question
A solid cylinder has total surface area of 462 cm2. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.
Solution
We have
Curved surface area = `1/3` × total surface area
⇒ `2πrh = 1/3(2 πrh + 2πr^2)`
⇒ `6πrh = 2πrh +2πr^2`
⇒ `4πrh =2πr^2`
⇒ 2h = r
We know that,
Total surface area = 462
⇒ Curved surface Are = `1/3`× 462
2πrh =154
⇒ `2× 3.14× 2h^2 = 154`
⇒ `h^2=(154× 7)/(2× 22× 2)`
⇒ `49/4`
⇒ h=`7/2`cm
⇒ r=2h
⇒ r=`2× 7/2cm`
⇒ r=7cm.
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