Question

# 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=6×2πr2⇒8πrh=12πr2⇒2h=3r⇒r=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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