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Question
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
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Solution
Let r and h be the radius and height of the solid cylinder respectively.
Given, r + h = 37 cm
The total surface area of the cylinder = 1628 cm2 (Given)
∴ `2pir(r + h) = 1628`cm2
⇒ `2pir xx 37 = 1628` cm2
⇒ `2 xx 22/7 xx r xx 37 = 1628`cm2
⇒ `r = (1628 xx 7)/(2 xx 22 xx 37) = 7` cm
rth = 37 cm ⇒ 7 + h = 37 cm ⇒ h = 30 cm
The volume of the cylinder = `pir^2h`
= `22/7 xx 7 xx 7 xx 30 = 4620` cm3
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