The volume of the large cube is 5³ = 125 cm³. The volume of each small cube is 1³ = 1 cm³. The number of small cubes is the total volume divided by the volume of each small cube: 125 cm³ / 1 cm³ = 125 cubes. The surface area of the large cube is 6 × side² = 6 × 5² = 6 × 25 = 150 cm². The surface area of one small cube is 6 × side² = 6 × 1² = 6 cm². The sum of the surface areas of all the smaller cubes is the number of small cubes multiplied by the surface area of one small cube: 125 × 6 = 750 cm².
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of surface areas of the smaller cubes ?
Asked in GPSC Prelims CSP 1 2017 · Topic: Measurement/Unit (Derived Units and their Expression)
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