Question

How much material is required to wrap a cubical box of side
A.7.5 m
B.12 cm

Answer 1

Hint: Calculate the surface area of the cubical box which is required to be wrapped. The surface area of a cube is given by the formula \[A = 6{a^2}\] , where \[a\] is the length of the side of the cube.
In this question the length of the sides of two different cubes are given and as we know the total surface area of a cube give the sum of area of all its 6 faces so we can calculate the required amount of material to be used to wrap the box by finding the surface area of both the box separately.

Complete step-by-step answer:
A.7.5 m
Given the side of the cubical box to be wrapped \[a = 7.5\]
So the surface area of the cubical box which is required to be wrapped will be
 \[
\Rightarrow A = 6{a^2} \\
   = 6 \times {\left( {7.5} \right)^2} \\
   = 337.6\;{m^2} \;
 \]
Hence the total material required to wrap the cubical box of side 7.5m is \[ = 337.6{m^2}\]
So, the correct answer is “ \[ = 337.6\;{m^2}\] ”.

B.12 cm
Given the side of the cubical box to be wrapped \[a = 12\;cm\]
So the surface area of the cubical box which is required to be wrapped will be
 \[
\Rightarrow A = 6{a^2} \\
   = 6 \times {\left( {12} \right)^2} \\
   = 6 \times 144 \\
   = 864\;c{m^2} \;
 \]
Hence the total material required to wrap the cubical box of side 12 cm is \[ = 864\;c{m^2}\]
So, the correct answer is “ \[ = 864c{m^2}\] ”.

Note: Total surface area of a cube gives the total amount of material required to make a cube of 6 sides since a cube has 6 sides and the volume of a cube gives the total amount of material it can hold or the capacity it has. Total surface area is the sum of the area of each surface and it is multiplied with 6 since a cube has 6 sides to it.