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Question
The sum of the height and the radius of a cylinder is 28 cm and its total surface area is 616 cm2, find the volume of the cylinder.
Solution
Let height = h
radius = r
h+ r = 28cm ...(given)
∴ h = 28 - r cm
Total surface area of cylinder
= 2πrh + 2πr2
2πr(28 - r) + 2πr2 = 616
56πr - 2πr2 + 2πr2 = 616
56πr = 616
r = `(616)/(56pi)`
r = 3.5cm
h = 28 - r
= 28 - 3.5
= 24.5cm
Volume of cylinder
= πr2h
= π(3.5)2 x 24.5
= 943cm3
∴ Volume of cylinder is 943cm3.
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