# A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas

**Solution:**

Given: a solid cube of side 12 cm is cut into eight cubes of equal volume.

We have to find the side of the new cube and the ratio between their surface areas.

Since the solid cube is cut into eight cubes of equal volume, each smaller cube so obtained will have the one-eighth volume of the solid cube of side 12 cm.

For the ratio of their surface areas, we will find the surface area of the two types of cubes individually.

Volume of the cube of edge length 'a' = a^{3}

The surface area of the cube of edge lemgth 'a' = 6a^{2}

Edge of the solid cube, a = 12 cm

The volume of the solid cube = a^{3}

= (12 cm)^{3}

= 1728 cm^{3}

The cube is cut into 8 equal cubes of the same volume.

Volume of each small cube = (1/8) × 1728 cm^{3} = 216 cm^{3}

Let 'x' be the side of each small cube.

Volume of each small cube = x^{3} = 216 cm^{3}

x^{3} = (6 cm)^{3} [Since 6^{3} = 216]

x = 6 cm

Surface area of the solid cube = 6a^{2}

Surface area of the small cube = 6x^{2}

Ratio between their surface areas = 6a^{2}/6x^{2}

= a^{2}/x^{2}

= (a/x)^{2}

= (12/6)^{2}

= 4/1

The side of the new cube is 6 cm and the ratio between the surface areas is 4 : 1.

**Video Solution:**

## A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.5 Question 8:

**Summary:**

It is given that there is a solid cube of side 12 cm which is cut into eight cubes of equal volume. We have found that the side of the new cube is 6 cm and the ratio between the surface areas is 4:1.