A right circular solid cylinder has radius of base 7 cm and height is 28 cm. It is melted to form a cuboid such that the ratio of its side… — Answer & Discussion

A right circular solid cylinder has radius of base 7 cm and height is 28 cm. It is melted to form a cuboid such that the ratio of its side is 2 ∶ 3 ∶ 6. What is the total surface area (in cm²) cuboid?

A72 × (1078/9)^2/3
B36 × (2156/9)^2/3
C72 × (2156/9)^2/3
D36 × (1078/3)^2/3

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Discussion 1

CCommunity11 Jul 2019

Ratio of the sides of a cuboid is 2 ? 3 ? 6

Let the length, breath and height of a cuboid be 2x, 3x and 6x

Volume of solid cylinder = Volume of cuboid

⇒ πr2h = 2x × 3x × 6x

⇒ (22/7) × 7 × 7 × 28 = 36x3

⇒ x3 = (22 × 7 × 7) /9

⇒ x = [(22 × 7 × 7) /9]1/3

Total surface area of cuboid = 2(lb + bh + hl)

⇒ Total surface area of cuboid = 2(2x × 3x + 3x × 6x + 6x × 2x)

⇒ Total surface area of cuboid = 2(6x2 + 18x2 + 12x2)

⇒ Total surface area of cuboid = 2(36x2)

⇒ Total surface area of cuboid = 2 × 36 × [(22 × 7 × 7) /9]2/3

∴ Total surface area cuboid = 72 × (1078/9)2/3