Question

The surface area of a cube is $ 1176c{m^{2.}} $ find its volume.

Answer 1

Hint: Cube can be defined as the three-dimensional solid object surrounded by the six square faces or the sides with the three meeting at each vertex and has six faces, twelve edges and eight vertices. Here, first of all we will find the length of the side of the cube and then will find the volume of the cube.

Complete step-by-step answer:
Total surface area of the cube can be given by $ A = 6{l^2} $ , where “l” is the length of the cube.
Given that the total surface area of the cube $ = 1176c{m^2} $
Place the formula on the left hand side of the standard formula.
 $ 1176 = 6{l^2} $
When the number is multiplicative on one side if moved to the opposite side then it goes to division and vice-versa.
 $ {l^2} = \dfrac{{1176}}{6} $
Common factors from the numerator and the denominator cancel each other.
 $ \Rightarrow {l^2} = 196 $
Now, take square-root on both the sides of the above equation.
 $ \Rightarrow \sqrt {{l^2}} = \sqrt {196} $
Square and square-root cancel each other on the left hand side of the equation-
 $ \Rightarrow l = \sqrt {{{14}^2}} $
Now, we know that $ 196 $ is the square of the term $ 14 $ , square and square cancel each other.
 $ \Rightarrow l = 14cm $
Now, the volume of the cube can be given by –
 $ V = {l^3} $
Place the values in the above expression –
 $ V = {(14)^3} $
Simplify the above expression –
 $ V = 2744c{m^3} $
This is the required solution.
So, the correct answer is “ $ V = 2744c{m^3} $ ”.

Note: Always remember all the formulas for the volume and area for the closed and open figures. Know the difference between the volume and the areas of the figures. Volume is measured in cubic units whereas the area is measured in the square units. Always put the appropriate unit once the value is calculated as the final answer. Remember squares and cubes of the numbers till at least twenty.