Question

The floor of a rectangular hall has a perimeter 250m. If the cost of painting the four walls at the rate of Rs. 10 per m2 is Rs. 15000, find the height (in cm) of the hall.

Answer 1

Hint: let us find the area of four walls. Area of four walls of the rectangular hall is the lateral surface area whose value = 2h (l + w), where h, l, w is the height, length and width of the rectangular hall respectively. Here is the figure of the rectangular hall with height h, length l and width w.

Complete step-by-step solution:
Now, here we are given the total cost of painting and the rate of painting per ${m}^{2} $. So,
Total cost = Rate x Total area
Total cost = 15000, Rate = 10 per ${m}^{2}$,
So, area = total cost / rate = 15000 / 10 = 1500 ${m}^{2}$
So, area of four walls = 1500 ${m}^{2}$
Now, area of four walls = lateral surface area = 2h (l + w)
Also, perimeter of rectangular hall = 2(l + w) =250 m
So, area of walls = h (250) m
\[ \Rightarrow \] $1500 {m}^{2} $ = h (250) m
\[ \Rightarrow \] h = 6m
Now, 1m = 100cm
\[ \Rightarrow \] h = 600cm
So, the height of the hall is 600 cm.

Note: In such types of questions, students generally use total surface area instead of lateral surface area. In this question it is said that the four walls of a hall are to be painted and not the ceiling and the floor. If it is written in the question that the ceiling and floor along with walls have to be painted then we will use the formula of total surface area.