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?
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Answer:
ratio of surface area of bigger cube to that of the smaller cubes = 1:5
Step-by-step explanation:
volume of bigger cube = a³ = 5³ = 125 cm³
volume of smaller cube = a³ = 1³ = 1 cm³
no. of smaller cubes = 125/1 = 125 cubes
surface area of bigger cube = 6a² = 6(5²)
= 6(25)
= 150 cm²
surface area of 1 smaller cube = 6a² = 6(1²) = 6cm²
surface area of 125 smaller cubes = 6 × 125
= 750 cm²
ratio = 150 : 750
= 1 : 5
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