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

Step-by-step explanation:

We start with a 5cm cube. Each surface area is 25cm². There are 6 surfaces on a cube therefore the total surface area is 6 x 25cm² = 150 cm².

The 5 cm cube is deconstructed to make 1 cm cubes. There will be a total of 150 of these 1 cm cubes. One side of these cubes is 1 cm² therefore each 1 cm cube has a total surface area of 6 x 1 cm² = 6 cm².

Since there are 150 of the 1 cm cubes the total surface area of the 1 cm cubes is 150 x 6 cm² = 900 cm².

Therefore the ratio of the surface area of the large cube to the total surface area of the small cubes is 150/900 or 1/6.

Edit: Correction : there is only 125 of the small cubes for a total surface area of 125 x 6 = 750 cm². Therefore the ratio should be 150/750 or 1/5