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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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