Example 5 The internal measures of a cuboidal room are 12 m Γ 8 m Γ 4 m. Find the total cost of whitewashing all four walls of a room, if the cost of white washing is Rs 5 per π^2. What will be the cost of white washing if the ceiling of the room is also whitewashed.
Given,
Length of room = π = 15 m
Breadth of room = π = 10 m
& Height of room = β = 7 m
To find cost of whitewashing,
first we find area to be whitewashed
Finding Area to be whitewashed
Given that 4 walls and ceiling is whitewashed
So,
Area Painted = Area of 4 walls + Area of top ceiling
Area of 4 walls
Area of 4 walls
= 2β(π+π)
= 2Γ4Γ(12+8)
= 2Γ4Γ20
= 160 m2
Area of ceiling
Area = Length Γ Breadth
= 12 Γ 8
= 96 m2
Thus,
Area of 4 walls = 160 m2
Area of 4 walls + Area of ceiling = 160 + 96
= 256 m2
Now,
we need to cost of painting the 4 walls, and also the cost of painting the walls + Ceiling
Cost of painting the 4 walls
Given that
Cost of white washing is Rs 5 per m2
So,
Cost of white washing 1 m2 = Rs 5
Cost of whitewashing 160 m2 = Rs 5 Γ 160
= Rs 800
So, Rs 800 is required to paint the 4 walls
Cost of painting the 4 walls + Ceiling
Cost of white washing 1 m2 = Rs 5
Cost of whitewashing 256 m2 = Rs 5 Γ 256
= Rs 1280
So, Rs 1280 is required to paint the 4 walls + Ceiling

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.