Question

If the total surface area of a cube is $150c{{m}^{2}}$ , find the edge.

Answer 1

Hint: In order to solve this problem, we need to find the formula of the surface area of the cube in terms of the side of the cube. The formula for the surface area of the cube is given by $\text{Surface area}=6\times {{\left( x \right)}^{2}}$ , where x is the side of the cube. Also, the formula for the area of the square is given by $\text{Area = }{{\left( \text{side} \right)}^{\text{2}}}$ .

Complete step by step answer:
We are given the surface area of the cube.
And we are asked to find the side of the cube.
Let's formulate the surface area in terms of the side of the cube.
Let the side of the cube be x cm.
It can be shown as follows,

We can see from the diagram a cube is formed by 6 faces.
The six faces are as follows, front, back, left, right, top, bottom.
The property of the cube is that the cube has all the sides of the same length.
Also, we can see that each side of the cube is square.
We already know the area of the square.
Area of the square is given by $\text{Area = }{{\left( \text{side} \right)}^{\text{2}}}$ .
The surface area of the cube is, in fact, the area surrounds the cube.
As it seems that the cube is surrounded by 6 faces.
Hence the surface area would be the sum of all the 6 faces.
Hence, we can say that,
$\text{Surface area}=6\times \text{area of square}$
We also know the area of the square, hence, substituting it we get,
$\text{Surface area}=6\times {{\left( x \right)}^{2}}$
Substituting the values of surface area, we get,
$150=6\times {{x}^{2}}$
Solving the equation, we get,
${{x}^{2}}=\dfrac{150}{6}=25$ .
Taking square root on both sides we get,
x = 25 cm.

Hence, the edge of the cube is 5 cm.

Note: We need to count the sides of the cube properly. Also, in the end, while taking the square root there are two possibilities, that is +5 and -5. But we instead choose +5 because it is the distance of the cube and it can never be negative.