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Directions: Read the condition given below and answer the question based on it.Three cubes of volume 216 cm cube is placed one after another. The total surface area of resulting cuboids is what percent of the surface area of the single cube?1. 233 \(\frac{1}{3}\)%2. 189 \(\frac{1}{3}\)%3. 288 \(\frac{1}{3}\)%4. 169 \(\frac{1}{3}\)% |
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Answer» Correct Answer - Option 1 : 233 \(\frac{1}{3}\)% Given: The volume of each cube is 216 cm cube Formula Used: Side = ∛Volume of cube Surface area of cube = 6 × (side) 2 Total Surface area of cuboids = 2 × (lb + bh + hl) Required percentage = (First quantity/second quantity) × 100 Calculation: The volume of cube is 216 cm cube ∴ Side of cube = ∛ 216 = 6 cm Now, surface area of cube = 6 × (6) 2 = 216 cm square When three cubes are place side by side so, the breadth and height of resulting cuboids will be same as cube but length will change ∴ Length of cuboid = 6 + 6 + 6 = 18 cm So, length = 18 cm, breadth = 6 cm and height = 6 cm ∴ Total Surface area of cuboids = 2 × (18 × 6 + 6 × 6 + 6 × 18) = 504 cm square Now, required percentage = (504/216) × 100 = 233\(\frac{1}{3}\)% Hence, option (1) is correct |
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