A solid cylinder has a total surface area of 231 cm². Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.
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Answer:
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Given : Total surface area of cylinder, T.S.A = 231 cm²
Curved surface area = 2/3(Total surface area)
Curved surface area = 2/3 x 231 = 154
So, Curved surface area = 2πrh = 154 cm² ……….…(1)
Total surface area of cylinder = 2πrh + 2πr²
2πrh + 2πr² = 231
154 + 2πr² = 231
[From eq 1]
2πr² = 231- 154
2 x 22/7 x r² = 77
44/7 r² = 77
44r² = 77 × 7
r² = (77 × 7)/44
r² = (7 × 7)/4
r² = 49/4
r = √49/4
r = 7/2
Put this value of r = 7/2 in eq 1,
2πrh = 154
2 x 22/7 x 7/2 x h = 154
22 h = 154
h = 154/22
h = 7
Now,
Volume of the cylinder , V = πr²h
V = 22/7 x 7/2 x 7/2 x 7
V = 11 × 49/2
V = 539/2
V = 269.5
Hence, the volume of the cylinder is 269.5 cm³
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