Question

What is the total surface of a cube whose side is $0.5cm$ ?
\[\begin{array}{*{35}{l}}
   \left( a \right)1.5c{{m}^{2}} \\
   \left( b \right)0.25c{{m}^{2}} \\
   \left( c \right)0.125c{{m}^{2}} \\
   \left( d \right)2.5c{{m}^{2}} \\
\end{array}\]

Answer 1

Hint: In this question, we are given a cube whose side is $0.5cm$. We have to find total surface of the cube which means we have to find surface area of all six faces of the cube. We will use the formula for finding the total surface area of the cube when side is given. Formula of total surface area of a cube when the side is give, is given by –
Total surface area of cube $=6{{a}^{2}}$, where $a$ is the side of cube.

Complete step by step answer:
Here, we are given a cube of side $0.5cm$, and we have to find the total surface of the cube. Total surface of the cube means we have to find the surface area of all six faces of the cube.
Formula for finding total surface area of a cube when the side is give, is given by –
Total surface area of the cube $=6{{a}^{2}}$, where $a$ is the side of the cube.
We are given the side as $0.5cm$. Therefore, $a=0.5cm$.
Total surface area of cube
 \[\begin{align}
  &\Rightarrow A =6{{a}^{2}} \\
 & \Rightarrow A=6{{\left( 0.5 \right)}^{2}} \\
 & \Rightarrow A=6\left( 0.5 \right)\times \left( 0.5 \right) \\
 &\Rightarrow A =1.5c{{m}^{2}} \\
\end{align}\]

So, the correct answer is “Option A”.

Note: If students cannot remember the formula for surface area of the cube, then they should imaging one face of the cube. Since one face represents a square, therefore area of square of side $a$ will be ${{a}^{2}}$. Similarly, for six faces, area becomes ${{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}+{{a}^{2}}=6{{a}^{2}}$. Since all six faces make up the total surface area of the cube, the total surface area of the cube becomes $6{{a}^{2}}$. Students should not get confused with curved surface area and total surface area. Curved surface area represents area of four faces of a cube and hence is given by formula $4{{a}^{2}}$, whereas total surface area represents area of all six faces of a cube and hence is given by $6{{a}^{2}}$. Don’t make mistakes while squaring the decimal numbers.