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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?1). 72 × (1078/9)2/32). 36 × (2156/9)2/33). 72 × (2156/9)2/34). 36 × (1078/3)2/3 |
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Answer» 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 |
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