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A solid cylinder has the total surface area 231 square cm. If its curved surface area is 2/3 of the total surface area, then the volume of the cylinder is
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- 154 cu. cm.
- 308 cu. cm.
- 269.5 cu. cm
- 370 cu. cm
- 154 cu. cm.
Correct Option: C
Let the radius of cylinder be r cm.
Height = h cm.
According to the question,
2πrh + 2πr² = 231
Again, 2πrh = | × 231 = 154 | |
3 |
∴ 2πr² = 231 – 154
⇒ 2 × | r² = 77 | |
7 |
⇒ r² = | = | ||
22 × 2 | 2 × 2 |
⇒ r = | cm. | |
2 |
∴ 2πrh = 154
⇒ 2 × | × | × h = 154 | ||
7 | 2 |
⇒ 22h = 154
⇒ h = | = 7 cm. | |
22 |
∴ Volume of cylinder = πr²h
= | × | × | × 7 | cu.cm. | |||||
7 | 2 | 2 |
= 269.5 cu. cm.