If the volume of a cylinder is 154 times its height, then find the radius of the cylinder.
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The curved surface area of a cylinder is 154 cm2.
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asked Dec 29, 2017 in Class IX Maths by ashu Premium (930 points)
The curved surface area of a cylinder is 154 cm2. The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder.
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answered Dec 29, 2017 by saurav24 Expert (1.4k points)
Since curved surface area of a cyclinder = 154 cm2 [given]
Total surface area of cyclinder = 3 × curved surface area
2πrh + 2πr2 = 3 × 154
154 + 2πr2 = 462
2πr2 = 462 - 154 = 308
r2 = 308 × 7 / 2 × 22 = 49
r = 7 cm
Now, 2πrh = 154
2 × 22 / 7 × 7 × h = 154
h = 154 / 44 = 3.5 cm
∴ Volume of cyclinder = πr2h
= 22 / 7 × 7 × 7 × 3.5 = 539 cm3