Question

Find the surface area of a cube with edge: $(i)11cm$(ii)$1.2m$ (iii) $27cm$

Answer 1

Hint: We have given the edge of the cube. We will put the value of edge in the formula of surface area to get the desired result. By using the formula of surface area of cube $ = 6 \times {a^2}$, where a $ = $edge length


Complete step by step solution:
(i) Given: Edge of cube (a)$ = 11cm$
Now, we will use formula of cube, and put the value of a in the formula, we have total surface area of a cube $\left( {T.S.A} \right) = 6 \times {\left( a \right)^2}$
$
  T.S.A = 6 \times {\left( {11} \right)^2} \\
  T.S.A = 6 \times 121 \\
  T.S.A = 726c{m^2} \\
 $
Therefore, $T.S.A$ of a cube is $726c{m^2}$.
(ii) Given: Edge of a cube $\left( a \right) = 1.2m$
Formula of total surface area of cube $\left( {T.S.A} \right) = 6c{m^2}$
Now, we will substitute the value of ‘$a$’ in the above formula, we have
$T.S.A = 6 \times {\left( {1.2} \right)^2}$
$
   = 6 \times 1.44 \\
   = 8.64c{m^2} \\
 $
Thus, the required answer of $T.S.A = 8.64{m^2}$
(ii) Edge of a cube $\left( a \right) = 27cm$ (given)
Use the formula of total surface area of a cube for calculating the side of a cube.
So, total surface area of cube $\left( {T.S.A} \right) = 6 \times {\left( a \right)^2}$
$
  T.S.A = 6 \times {\left( {27} \right)^2} \\
  T.S.A = 6 \times 729 \\
  T.S.A = 4,374c{m^2} \\
 $
Hence,$T.S.A$ of cube is $4,374c{m^2}$
Additional information: Cube is a solid, three – dimensional figure, which has $6$ square face, $8$ vertices and $12$ edges. It is also said to be a regular hexahedron.


Note: Students must put the correct value of the side of a cube in the formula of total surface area of a cube and also write the proper units associated with the final answer.If you put the wrong value then you will not be able to find the correct answer.