Question

A room is \[8m\] long, \[6m\] broad and \[5.5m\] height. It has one of the dimensions \[2.5m\] by \[2m\] and 2 windows each of dimensions \[1.5m\] by \[1m\]. Find the cost of whitewashing the walls at \[Rs.3.20\;{\text{per sq}}{\text{.m}}\].

Answer 1

Hint:In this question, the given is the length, breadth, and height of the room and also gives the dimensions of the room and windows. We have to find the cost of whitewashing the room. We have the cost of whitewashing the wall with \[Rs.3.20\;{\text{per sq}}{\text{.m}}\].First we have to find the surface area of a room to be whitewashed and multiply the cost to the surface area of the room to find the total cost to whitewashing the room.

Complete step-by-step answer:

Here, it is given that A room is \[8{\text{ }}m\] long, 6m broad and \[5.5m\] height
And one door dimensions \[2.5m\] by \[2{\text{ }}m\]
And 2 window dimensions \[1.5{\text{ }}m\] by \[1{\text{ }}m\]
We have to find the cost of the whitewashing
So, first lateral surface area of room
We know the lateral surface area cuboid \[ = 2h\left( {l + b} \right)\]
Putting the value
\[ = 2h\left( {l + b} \right)\]
\[ = 2 \times 5.5\left( {8 + 6} \right)\]
\[ = 264{\text{ }}{m^2}\]
Again, we have to find the area of door
Area of door \[ = l \times b\]
Where l= 2 m and b= 2.5 m
\[ = 2 \times 2.5\] \[ = 5{\text{ }}{m^2}\]
And area of 2 windows=\[ = 2 \times l \times b\]
Where l= 1.5m and b= 1m
\[ = 2 \times 1.5 \times 1\]
\[ = 3{\text{ }}{m^2}\]
\[{\text{Area of walls to be whitewashed = Area of walls - Area of door and 2 windows}}\]
Area of walls to be whitewashed \[ = 264 - 5 - 3\] \[ = 256{\text{ }}{m^2}\]
Now, we have the cost of whitewashing the walls at Rs.3.20 per square meter
so, cost of whitewashing \[ = 256 \times 3.2\] \[ = Rs.{\text{ }}819.2\]
Hence, cost of whitewashing is \[Rs.{\text{ }}819.2\]

Note:Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a given service. A cost price includes all outlays that are required for production, including property costs, materials, power, research and development, testing, worker wages and anything else that must be paid for that.Students should remember important formula of lateral surface area of cuboid to solve these types of questions.