Find the total cost of whitewashing the 4 walls of a cuboidal room at the rate Rs.15 per \[{{m}^{2}}\]. The internal measures of the cuboidal room are length 10m, breadth 4m, and height 4m.

Question

Find the total cost of whitewashing the 4 walls of a cuboidal room at the rate Rs.15 per $${{m}^{2}}$$. The internal measures of the cuboidal room are length 10m, breadth 4m, and height 4m.

Vedantu Content Team · Accepted Answer

Hint: First of all, find the area of the four walls of the cuboidal room by using 2h (l + b). Now, multiply this area of the four walls by the cost of whitewashing per \[{{m}^{2}}\] to get the total cost of whitewashing.

Complete step-by-step answer:

Here, we have to find the total cost of whitewashing the 4 walls of a cuboidal room at the rate of \[Rs.15/{{m}^{2}}\]. Given that internal measures of the cuboidal room are length 10m, breadth 4m, and height 4m.
In this question, we have to whitewash the 4 walls of the cuboidal room. In other words, we can say that we have to whitewash the lateral surface area of the cuboidal room while it is nothing but the total surface area of the cuboid except the upper face (ceiling) and lower face (floor).
We know that the lateral surface of the cuboidal 2h(l + b)…..(i) where h, l, and b are height, length, and breadth of the cuboid.

We are given that the height of the cuboidal room = h = 4m
Length of the cuboidal room = l = 10m
Breadth of the cuboidal room = b = 4m
So, by substituting the value of l = 10m b = 4m and h = 4m in equation (i), we get,
Lateral surface area or area of four walls of the cuboidal room = 2h (l + b)
\[=2\times 4\left( 10+4 \right)\]
\[=8\left( 14 \right)\]
\[=112{{m}^{2}}\]
So, we get the area of the four walls of the cuboidal room as \[112{{m}^{2}}\].
Now, we are given that the rate of whitewashing is \[15/{{m}^{2}}\].
That is, for \[1{{m}^{2}}\], the rate of whitewashing = Rs. 15.
So, for whitewashing the 4 walls of the cuboidal room, the cost = (Total surface area of the 4 walls) \[\times \] Rs. 15.
So, we get the total cost of the whitewashing 4 walls of the room = (112) (Rs. 15) = Rs. 1680.
Hence, we get the total cost of whitewashing as Rs. 1680.

Note: In this question, first of all, note that in a formula, units of all dimensions must be equal. Also, in this question, many students use the formula 2 (lb + bh + hl) which is wrong because this is the formula for the total surface area of the cuboid and not just the 4 walls. If we subtract the area of the upper and lower face that is 2 lb from the total surface area, we get the lateral surface area.