The length, breadth and height of a room are 5 m, 4 m, and 3 m respectively. Find the cost of white washing the walls of the room and ceiling at the rate of ₹7.50 per m2.
Solution:
Given: The length, breadth, and height of a room are 5 m, 4 m, and 3 m respectively.
Since the four walls and ceiling are to be whitewashed so, it has 5 faces only, excluding the base.
Hence, the area of the room to be whitewashed can be obtained by adding the area of the ceiling to the lateral surface area of the cuboidal room.
Lateral surface area of cuboid = 2(l + b)h
The cost of whitewashing the walls of the room and ceiling will be equal to the area of the room to be whitewashed multiplied by the rate of the whitewashing per m2.
Length, l = 5 m
Breadth, b = 4 m
Height, h = 3 m
Surface area of 5 faces = Area of the 4 walls and ceiling = lb + 2(l + b)h
lb + 2(l + b)h = (5 m × 4 m) + 2 × (5 m + 4 m) × 3 m
= 20 m² + 2 × 9 m × 3 m
= 20 m² + 54 m2
= 74 m²
The cost of whitewashing the walls of the room and ceiling = Rate × Area
= ₹ 7.50 / m² × 74 m2
= ₹ 555
Thus, the cost of whitewashing the walls of the room and the ceiling is ₹555.
☛ Check: Class 9 Maths NCERT Solutions for Chapter 13
Video Solution:
The length, breadth and height of a room are 5 m, 4 m, and 3 m respectively. Find the cost of white washing the walls of the room and ceiling at the rate of ₹7.50 per m².
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.1 Question 2
Summary:
It is given that the length, breadth and height of a room are 5 m, 4 m, and 3 m respectively. We have found that the area of whitewashing is 74 m² and the total cost of whitewashing the walls of the room and the ceiling is ₹555.
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