Question

A swimming pool is \[25\] m long, \[20\] m wide and \[2\] m deep. Find the cost of cementing its floor and the four walls at the rate of Rs. \[20\] per sq. m.

Answer 1

Hint: Let us consider the length, width and height of a cuboid is \[l\], \[b\] & \[h\] respectively.
So, the area of the four walls is \[2(l + b)h\] and the area of its floor is \[lb\].
After calculating the area of the swimming pool we will the total cost of cementing.

Complete step-by-step answer:
It is given that; a swimming pool is \[25\] m long, \[20\] m wide and \[2\] m deep. We have to find the cost of cementing its floor and the four walls at the rate of Rs. \[20\] per sq. m.
Let us consider the length, width and height of a cuboid is \[l\], \[b\] & \[h\] respectively.
So, the area of the four walls is \[2(l + b)h\] and the area of its floor is \[lb\].
Therefore, the area of the four walls and floor is \[2(l + b)h + lb\] sq. m.
Which is nothing but the area of the swimming pool.
Let us substitute \[l = 25\], \[b = 20\] & \[h = 2\] in the general formula of the area of four walls and the floor, then we get,
The area of the swimming pool is \[2(25 + 20) \times 2 + 25 \times 20\] sq. m.
On simplifying the area we get, the area is \[680\] sq. m.
Now, it is given that the cost of cementing is Rs. \[20\] per sq. m.
Therefore, the total cost of cementing is Rs. \[20 \times 680\].
Hence we get, the total cost is Rs. \[13600\].
Hence, the total cost of cementing of the four walls and the floor of the given swimming pool is Rs. \[13600\].

Note: The area of the four walls of a cuboid is known as the lateral surface of the cuboid. Hence we use the lateral surface area to find the area of the four walls. And we know that the sum of all the area is the total area that is required to be cemented.