Question

Find the length of the side of a cube whose total surface area is $ 216 $ square cm.

Answer 1

Hint: Cube is 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. Use the general formula for the total surface area of the cube, $ A = 6{l^2} $ , where “l” is the length of the cube.

Complete step-by-step answer:

Given that the total surface area of the cube $ = 216c{m^2} $
Place the formula on the left hand side of the above equation.
 $ 6{l^2} = 216 $
When the number in multiplicative changes its side, it goes to division and vice-versa.
 $ {l^2} = \dfrac{{216}}{6} $
 $ \Rightarrow {l^2} = 36 $
Now, take square-root on both the sides of the equation.
 $ \Rightarrow \sqrt {{l^2}} = \sqrt {36} $
Square and square-root cancel each other on the left hand side of the equation-
 $ \Rightarrow l = \sqrt {{6^2}} $
Now, we know that $ 36 $ is the square of $ 6 $ , square and square cancels each other.
 $ \Rightarrow l = 6cm $
Hence, the required answer is length of the cube is $ 6cm $

Note: The squares and the square roots are opposite to each other and so cancel each other. Perfect square number is the square of an integer, simply it is the product of the same integer with itself. For example - $ 25{\text{ = 5 }} \times {\text{ 5, 25 = }}{{\text{5}}^2} $ , generally it is denoted by n to the power two i.e. $ {n^2} $ . The perfect square is the number which can be expressed as the product of the two equal integers. For example: $ 9 $ , it can be expressed as the product of equal integers. $ 9 = 3 \times 3 $ . Remember the difference between the area and total surface area of any object.