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2 cubes each of volume 64 cm3 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 = 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 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 be 'a'

Therefore, volume of the cube = a3

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.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 13

Video Solution:

2 cubes each of volume 64 cm³ 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

Summary:

The surface area of the resulting cuboid if 2 cubes each of volume 64 cm3 are joined end to end is 160 cm2.

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