Question

A toy is made with seven equal cubes of sides $ \sqrt 7 $ cm. Six cubes are joined to six faces of a seven cube. Find the total surface area of the toy.

Answer 1

Hint: Here first of all we will find the surface area of one side of the cube and then will frame the formula for when six cubes joined to six faces of seventh cube then five faces of six cubes are available and then place the values and simplify for the resultant value.

Complete step by step solution:
First of all find the surface area of the cube $ = 6 \times sid{e^2} $
We are given that side $ = 6.{\left( {\sqrt 7 } \right)^2} = 6.7 = 42\;c{m^2} $
Surface area of one side of the cube $ = {(\sqrt 7 )^2} $
Always remember that the square and square root cancel each other.
Therefore, surface area of one side of the cube $ = 7\;c{m^2} $
Now, when six cubes are joined with the six faces of the seventh cube then five faces of six cubes are available-
So, the total surface area of the toy is $ = 6 \times 5 \times sid{e^2} $
Place the values in the above equation-
Total surface area $ = 6 \times 5 \times {\sqrt 7 ^2} $
Square and square root cancel each other. Simplify the above expression -
Total surface area $ = 210\;c{m^2} $
This is the required solution.
So, the correct answer is “ $ 210\;c{m^2} $ ”.

Note: The above example can be solved by using the other method such as first finding the surface area of seven cubes and then subtracting the value of the area of twelve faces (since six faces are joined together with other six faces and therefore twelve faces are reduced) and then simplify for the resultant value.