If a cube is divided into 9 cubes each having a diagonal of value 6√3. Find the surface area of a rectangle formed by joining two of these big cubes.
Answers
Given,
Diagonal of a small cube = 6√3 cm
(As you've not specified the unit, I am taking it as cm)
To find,
The Surface area of a rectangle formed by joining two big cubes
Solution,
Diagonal of a cube with edge a => a√3
=> 6√3 = a√3
=> a = 6 cm
So, the length of the edge of the small cube = 6 cm
If we put the 9 small cubes together into one big cube (like in the attached figure), the length of the edge of that cube will be => 6+6+6 = 18 cm
When we join 2 of these cubes,
we get a rectangle with length = 18+18 = 36 cm
breadth = 18cm and height = 18cm
The formula for surface area of a rectangle is => 2(lb+bh+hl)
By putting the appropriate values, we get
Surface area = 2( 36*18 + 18*18 + 18*36 )
= 2( 648 + 324 + 648 )
= 2(1620)
= 3240 cm²
Therefore, the surface area of the rectangle is equal to 3240 cm².
