A cube of side 5 cm is cut into as many 1 cm cubes as possible. What i

1.	A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface areas of the original cube to that of the sum of the surface areas of the smaller cubes?
Answer» Surface area of a cube = 6 a², where a is side of a cube. .^.. Side of cube = 5 cm .^.. Surface area of the cube = 6 x (5)² = 6 x 25 = 150 cm² Now, surface area of the cube with side 1 cm = 6 x (1)²= 6 cm² .^.. Surface area of 5 cubes with side 1 cm = 5 x 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

A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface areas of the original cube to that of the sum of the surface areas of the smaller cubes?

Answer»

Surface area of a cube = 6 a², where a is side of a cube.

.^.. Side of cube = 5 cm

.^.. Surface area of the cube = 6 x (5)²

= 6 x 25

= 150 cm²

Now, surface area of the cube with side 1 cm = 6 x (1)²= 6 cm²

.^.. Surface area of 5 cubes with side 1 cm = 5 x 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