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Question

# A solid cylinder has total surface area of 462cm2. Its curved surface area is one-third of its total surface are. Find the volume of the cylinder (Take π=227)

A
224
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B
845
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C
664
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D
None of the above
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Solution

## The correct option is D None of the aboveGiven, total surface area of cylinder = 462 square cm.Also, CSA of cylinder =TSA of cylinder3⇒TSA=2πrh+2πr2⇒TSA=CSA+2πr2⇒TSA=TSA3+2πr2⇒2TSA3=2πr2⇒TSA3=πr2⇒4623=227×r2⇒r=7cm Now, CSA of cylinder =TSA of cylinder3=4623=154cm2⇒2πrh=154⇒2×227×7×h=154⇒h=72cmTherefore, volume of the cylinder =πr2h=227×72×72=539cm3Hence, volume of the solid cylinder is 539cm3.

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