Two cubes, each of volume 64 cm3, are joined end to end. Find the total surface area of the resulting cuboid.
volume of each cube = 64 cm3
Let a be the side length of each cube
∴ a3 = 64
a = 4 cm
The figure shows both the cubes joined together after joining we get a cuboid of length 2a and breadth a and height a
Length of cuboid formed = l = 2a
l = 8 cm
Breadth of cuboid formed = b = 4 cm
Height of cuboid formed = h = 4 cm
In the cuboid so formed there are 4 rectangular surfaces of length l = 8 and breadth b = 4 and 2 square surfaces of length 4
Total surface area of cuboid = 4 × l × b + 2a2
= (4 × 8 × 4) + (2 × 42)
= 128 + 32
= 160 cm2
Total surface area of cuboid = 160 cm2