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Question

The radius of the base and the height of a cylinder are in the ratio of 2 : 3. If its volume is 12936 cm3, then the total surface area of the cylinder is

A
3080 cm2
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B
3480 cm2
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C
4260 cm2
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D
4860 cm2
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Solution

The correct option is A 3080 cm2
Since the ratio of the radius and the height is 2:3, we can assume the radius (r) = 2x and the height (h) = 3x

The volume of a cylinder is given by

πr2h=12936cm3

227(2x)2(3x)=12936

x=7

Hence,
radius of the base = 2×7=14 cm and
height of the base = 3×7=21 cm

Total surface area of the cylinder

= 2πr(r+h)

= 2π(14)(14+21)

=2×227×14×(35)=3080 cm2

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