# 2 cubes each of volume 64 cm^{3} are joined end to end. Find the surface area of the resulting cuboid

**Solution:**

We will find the length of the edge of each cube by using the formula for the volume of a cube = a^{3}, where the length of the edge is a.

As the cubes are joined end to end, they will appear as follows:

The surface area of a cuboid is the sum of areas of all its lateral faces.

Using the formula for the surface area of a cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively.

Let the length of the edge of each cube is a

Therefore, volume of the cube = a3

volume of the cube, a^{3} = 64 cm^{3}

a^{3} = 64 cm^{3}

a = ∛(64 cm^{3})

a = ∛(4 cm)^{3}

a = 4 cm

Therefore,

Length of the resulting cuboid, l = a = 4 cm

Breadth of the resulting cuboid, b = a = 4 cm

Height of the resulting cuboid, h = 2a = 2 × 4 cm = 8 cm

Surface area of the resulting cuboid = 2 (lb + bh + lh)

= 2 (4 cm × 4 cm + 4 cm × 8 cm + 4 cm × 8 cm)

= 2 (16 cm^{2} + 32 cm^{2} + 32 cm^{2})

= 2 × 80 cm^{2}

= 160 cm^{2}

Thus, the surface area of the resulting cuboid is 160 cm^{2}.

**Video Solution:**

## 2 cubes each of volume 64 cm^{3} are joined end to end. Find the surface area of the resulting cuboid

### NCERT Solutions Class 10 Maths - Chapter 13 Exercise 13.1 Question 1:

2 cubes each of volume 64 cm^{3} are joined end to end. Find the surface area of the resulting cuboid

The surface area of the resulting cuboid if 2 cubes each of volume 64 cm^{3} are joined end to end is 160 cm^{2}