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Question 114

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.


Solution

Let the radius and height of the cylinder be r and h respectively.
Curved surface area of cylinder =2πrh
Area of bases =πr2
Sum of areas of bases =2πr2
According to the question,
4×Curved surface area=6×Sum of areas of bases
=4×2πrh=6×2πr28πrh=12πr22h=3rr=23h
r=23×12=8 cm     [ h = 12 cm, given]
Curved surface area of the cylinder =2πrh
=2×227×8×12=44×8×127=603.428 cm2

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