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A right circular cylinder is formed. A = Sum of total surface area and the area of the two bases. B = Curved surface area of this cylinder. If A ∶ B = 3 ∶ 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

A right circular cylinder is formed. A = Sum of total surface area and the area of the two bases. B = Curved surface area of this cylinder. If A ∶ B = 3 ∶ 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder? Correct Answer 308

A = Sum of total surface area of cylinder and the area of the two bases

⇒ A = 2πr(r + h) + πr2 + πr2

⇒ A = 2πr2 + 2πrh + 2πr2

⇒ A = 4πr2 + 2πrh

B = the curved surface area of this cylinder

⇒ B = 2πrh

⇒ A ∶ B = (4πr2 + 2πrh) ∶ 2πrh

⇒ A/B = (4πr2 + 2πr h) / (2πrh)

⇒ 3/2 = (2r + h) / h

⇒ 3h = 4r + 2h

⇒ h = 4r

⇒ Volume of cylinder = πr2h

⇒ 4312 = πr2 4r

⇒ r3 = 4312 × (7/22) × 1/4

⇒ r = 7cm

⇒ Sum of area of the two bases of this cylinder = πr2 + πr2

⇒ Sum of area of the two bases of this cylinder = 2πr2

⇒ Sum of area of the two bases of this cylinder = 2 × (22/7) × 7 × 7

∴ Sum of area of the two bases of this cylinder = 308 cm2

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