Question

Two identical cubes each of volume 64 are joined together end to end to form a cuboid, the total surface are of the cuboid is

Answer 1

$\large\underline\bold{Given:}$

Volume of each smaller cube = 64 units^3

$\large\underline\bold{To~Find:}$

Area of resulting cuboid when two of such cubes are joined together side - by - side

$\large\underline\bold{Solution:}$


Volume of cube = 64 units^3
(Side)^3 = 64 units^3
(Side)^3 = (4 units)^3
Side = 4 units

Since,

The cubes are joined side of side so only the length of cuboid will be affected and the breadth and length will be the same as of cube.

Length of cuboid, l = 4 + 4 = 8 units
Breadth of cuboid, b = 4 units
Height of cuboid, h = 4 units

Now,

Total Surface Area of the cuboid ( TSA ) = 2 ( l * b + b * h + h * l )
TSA = 2 ( 8 * 4 + 4 * 4 + 4 * 8 )
TSA = 2 ( 32 + 16 + 32 )
TSA = 2 * 80
TSA = 160 units^2

Therefore,

Total surface area of the cuboid = 160 units^2