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प्रश्न
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?
उत्तर
Surface area of a cube = 6a2, where a is side of a cube.
... Side of cube = 5 cm
... Surface area of the cube = 6 × (5)2 = 6 × 25 = 150 cm2
Now, surface area of the cube with side 1 cm = 6 × (1)2 = 6 cm2
... Surface area of 5 cubes with side 1 cm = 5 × 6 = 30 cm2
Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes
= `30/150`
= `3/15`
= 1 : 5
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