$$2$$ cubes each of volume $$64$$ $$cm3$$ are joined end to end. Find the surface area of the resulting cuboid.

Question

Infinity Learn · Accepted Answer

We will find the length of the edge of each cube by using the formula for the volume of a cube = a³, where the length of the edge is 'a'.

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

2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid

Using the formula for the surface of 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 be 'a'.

Therefore, the volume of the cube = a³

The volume of the cube, a³ = 64 cm³

a³ = 64 cm³

a = ∛(64 cm³)

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 cm² + 32 cm² + 32 cm²)

= 2 × 80 cm²

= 160 cm²

Thus, the surface area of the resulting cuboid is 160 cm².

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.