Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its two bases. If its height is 12 cm, find its curved surface area.
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Base of a cylinder is a circle.
There are 2 bases in a cylinder.
Formulas used :-
- Area of base circle = πr²
- CSA of cylinder = 2πrh
Since there are 2 bases, area of bases = πr² + πr² = 2πr²
According to the question,
4 × (2πrh) = 6 × (2πr²)
→ 8πrh = 12πr²
Cancelling π on both sides,
→ 8rh = 12r²
→ 8r(12) = 12r²
Cancelling 12r on both sides
∴ r = 8 cm
For finding CSA:
CSA of cylinder = 2πrh
→ CSA of cylinder = 2π × 8 × 12
→ CSA of cylinder = 192π cm²
∴ CSA of cylinder = 192π cm²
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