Question

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?​

Answer 1

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