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Volume of a cube is 2744 cc. If two of its dimensions are doubled and the rest reduced by 300% then find out the ratio of the surface area between the original cube and the resultant figure.1. 6 : 52. 4 : 53. 7 : 54. 3 : 45. cannot be determined |
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Answer» Correct Answer - Option 1 : 6 : 5 Given: Volume of the cube = 2744 cc Formula used: Volume of cube = \({a^3}\) and surface area = \(6{a^2}\) Where, a = length of each side of the cube Surface area of cuboid = 2(lb + bh + lh) sq.cm. Where, l, b & h are the length, breadth and height of the cuboid respectively. Calculations: Volume of the cube = 2744 cc ∴ Length of each side = \(\sqrt[3]{{2744}}\) = 14 cm And, surface area = 6 × 142 = 1176 sq.cm. After the changes, dimensions are = (2 × 14), (2 × 14) and (1/4 × 14) ⇒ 28, 28, 7/2 cm respectively. [Since, one dimension is reduced by 300%, it will become 1/4 times of before] ∴ Surface area = 2(28 × 7/2 + 28 × 7/2 + 28 × 28) sq.cm. = 980 sq.cm. Required ratio = 1176 : 980 = 6 : 5 |
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