Question

2 cube each of volume 64 are joined end to end find the surface area of the resulting cuboid

Answer 1

Let l be the side of the cube
The volume of one cube =64 units
So,
l³= 64
l = ³√64
l = 4
So, the length of one cube = 4 units
Now, the cubes are joined end to end,
So the resulting cuboid's dimensions are:
length, l = 8 units
breadth, b = 4 units
height, h = 4 units
So,
the surface area of cuboid's = 2(lb+bh+hl)
= 2(8x4 + 4x4 + 4x8)
= 2( 32 + 16 + 32)
= 2(80)
= 160 sq. units
So the surface area of the resulting cuboid is 160 sq. units.

Answer 2

Volume of a cube = (side)^3 cubic units
volume= 64 = (a)^3 
Therefore, side of the cube = 4 units.

The cuboid formed by joining these two identical cubes will have dimensions->
length= (4+4) = 8, breadth= 4, height= 4
Surface area of a cuboid = 2*( l*b + b*h + l*h )
                                        = 2*( 32 + 16 + 32) = 2*80 = 160 sq units