Question

The total surface area of a cube is 600 $cm^2$. Find the lateral surface area of the cube.

Answer 1

Hint: Firstly, we will calculate the length of the cube l by comparing the given total surface area (T. S. A.) with its formula of total surface area of the cube: T. S. A. = 6$L^2$, where L is the length of the cube. After that, we will calculate the lateral surface area of the cube using the formula:
 L. S. A. = $4L^2$.

Complete step-by-step answer:
 We are given a cube whose total surface area is 600 $cm^2$.

For finding the length of the cube, we will compare this given T. S. A. with the formula of total surface area of the cube as 6$L^2$.
$ \Rightarrow $600 = $L^2$
Or, we can write it as
$ \Rightarrow $100 = $L^2$
Taking square roots both the sides, we get
$ \Rightarrow $L = 10 units
Now, when we have calculated the length of the cube, it is easier for us to find the value of the lateral surface area of the cube.
The formula of the lateral surface area of the cube L. S. A. is 4$L^2$.
Substituting the value of L in this formula, we get
$ \Rightarrow $L. S. A. of the cube = 4 $ \times $$(10)^2$.
$ \Rightarrow $L. S. A. of the cube = 4$ \times $100 = 400 $cm^2$.
Hence, the lateral surface area of the cube is found to be 400 $cm^2$.

Note: In such questions, you may get confused in the formulae of the lateral surface area and the total surface area of the cube. In a cube, LSA refers to the area of the lateral / curved surface area i.e., of only 4 sides while TSA refers to the area of the whole cube i.e., of all the 6 sides.