Question

Find the total surface area of a cube with a side 7 cm.

Answer 1

Hint: In this question, let us first draw the diagram of a cube with side 7 cm. Then from the formula of total surface area of a cube on substituting the given side length in the question and simplifying it further we get the result.

Complete step-by-step answer:
Now, from the given conditions in the question we have that side of a cube as 7 cm.

Surface Area:
Area covered by the outer surface of a solid.
Solid Figure:
The objects which occupy space ( i.e. they have three dimensions) are called solids.
Cuboid: A figure which is surrounded by six rectangular surfaces is called cuboid.
The cuboid shape has six sides called faces. Each face of a cuboid is a rectangle.
Cube: A cuboid whose length, breadth and height are same is called a cube
Let the side of a cube be a
The formula for total surface area of a cube of side a is given by
\[\text{Total Surface Area}=6{{a}^{2}}\]
Let us assume the total surface area of the given cube as A
Also assume that the given side of the cube in the question as a.
Now, on comparing the given values in the question with the above formula we get,
\[\Rightarrow a=7\]
\[\Rightarrow \text{A}=6{{a}^{2}}\]
Now, on substituting the value of a in the total surface area formula we get,
\[\Rightarrow \text{A}=6\times {{7}^{2}}\]
Now, this can be further written as
\[\Rightarrow \text{A}=6\times 49\]
Now, on further simplification we get,
\[\therefore \text{A}=294\]
Hence, the total surface area of the cube of side 7 cm is 294 ${cm}^{2}$.

Note: Instead of assuming some variable to the total surface area we can directly calculate it by substituting the value of the side in the respective formula.
It is important to note that we need to find the total surface area because considering 4 instead of 6 in the total surface area formula gives the lateral surface area which is completely different from the actual result.