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Question

A solid cylinder has the total surface area 231 sq.cm. If its curved surface area is of the total surface area, then the volume of the cylinder is

A 154 cu.cm Correct Answer Incorrect Answer
B 208 cu.cm Correct Answer Incorrect Answer
C 269.5 cu.cm Correct Answer Incorrect Answer
D 108.5 cu.cm Correct Answer Incorrect Answer

Solution

Total surface area = 231 cm2 Curved surface area = 2/3 x 231 = 154 cm2 Curved surface area of cylinder = 2πrh ⇒ 2πrh = 154 ⇒ 2 × (22/7) × r × h = 154 ⇒ r × l = 24.5 Total surface area of cylinder = 2πr(r + h) ⇒ 2πr(r + h) = 231 ⇒ r(r + h) = 36.75 ⇒ r2 + rh = 36.75 ⇒ r2 = 36.75 - 24.5 ⇒ r2 = 12.25 ⇒ r = 3.5 cm Volume of cylinder = πr2h ⇒ π × r × (r × h) ⇒ π × 3.5 × 24.5 ⇒ 269.5 cm ∴ The volume of the cylinder is 269.5 cm3 .

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