Answer
384.3k+ views
Hint: Here, we will find the area of the four walls of the cuboidal room along with the area of its rectangular ceiling by substituting the values of the dimensions of the given room. After finding the total area, we will multiply the cost of white washing \[1{{\rm{m}}^2}\] of a room by the total area to be covered by white washing.
Formula Used:
We will use the following formulas:
Area of four walls of a room \[ = 2h\left( {l + b} \right){{\rm{m}}^2}\], where \[h\] is the height , \[l\] is the length and \[b\] is the breadth of the wall.
Area of rectangular ceiling of a room \[ = \left( {l \times b} \right){{\rm{m}}^2}\], where \[l\] is the length and \[b\] is the breadth of the rectangle.
Complete step-by-step answer:
Let the length, breadth and height of the room be \[l,b\] and \[h\] respectively.
We will find the total area of the room by using the formula of area of four walls and ceiling of the room.
Therefore, we get
Total area of the four walls and the ceiling of the room \[ = 2h\left( {l + b} \right) + \left( {l \times b} \right){{\rm{m}}^2}\]……….\[\left( 1 \right)\]
Now, substituting \[l = 5\], \[b = 4\] and \[h = 3\] in the equation \[\left( 1 \right)\], we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 2\left( 3 \right)\left( {5 + 4} \right) + \left( {5 \times 4} \right)\]
Simplifying the expression, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 6 \times 9 + 20\]
Multiplying the term, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 54 + 20\]
Adding the terms, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 74{{\rm{m}}^2}\]
Now, according to the question, it is given that the cost of white washing the walls of the room and the ceiling at the rate of \[{\rm{Rs7}}{\rm{.50}}\] per \[{{\rm{m}}^2}\].
Hence, the cost of white washing \[1{{\rm{m}}^2} = {\rm{Rs7}}{\rm{.50}}\]
Therefore, the cost of white washing \[74{{\rm{m}}^2}\] \[ = {\rm{Rs}}7.50 \times 74 = {\rm{Rs}}555\]
Then the cost of white washing the walls of the room and the ceiling at the rate of \[{\rm{Rs7}}{\rm{.50}}\] per \[{{\rm{m}}^2}\] is Rs. 555.
Therefore, this is the required answer.
Note:
Here the shape of the room is not given but we will assume it to be a cuboid because the dimensions of the room are given as length, breadth, and height. A cuboid is a three dimensional shape whose sides are rectangular. In real life, rooms are usually in the shape of a cuboid but if in case all the 4 walls and the top and bottom of a room have the same length, breadth, and height, this would mean that it is cubical in shape as a cube has all the sides equal and square shaped. Some other examples of cuboidal figures which we see in our day to day life are matchboxes, shoeboxes, books, etc. All of these have a length, breadth and height respectively.
Formula Used:
We will use the following formulas:
Area of four walls of a room \[ = 2h\left( {l + b} \right){{\rm{m}}^2}\], where \[h\] is the height , \[l\] is the length and \[b\] is the breadth of the wall.
Area of rectangular ceiling of a room \[ = \left( {l \times b} \right){{\rm{m}}^2}\], where \[l\] is the length and \[b\] is the breadth of the rectangle.
Complete step-by-step answer:
Let the length, breadth and height of the room be \[l,b\] and \[h\] respectively.
![seo images](https://www.vedantu.com/question-sets/8acdb108-3578-4264-a349-5ce7d5356fb18166410991242883850.png)
We will find the total area of the room by using the formula of area of four walls and ceiling of the room.
Therefore, we get
Total area of the four walls and the ceiling of the room \[ = 2h\left( {l + b} \right) + \left( {l \times b} \right){{\rm{m}}^2}\]……….\[\left( 1 \right)\]
Now, substituting \[l = 5\], \[b = 4\] and \[h = 3\] in the equation \[\left( 1 \right)\], we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 2\left( 3 \right)\left( {5 + 4} \right) + \left( {5 \times 4} \right)\]
Simplifying the expression, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 6 \times 9 + 20\]
Multiplying the term, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 54 + 20\]
Adding the terms, we get
\[ \Rightarrow \] Total area of the four walls and the ceiling of the room \[ = 74{{\rm{m}}^2}\]
Now, according to the question, it is given that the cost of white washing the walls of the room and the ceiling at the rate of \[{\rm{Rs7}}{\rm{.50}}\] per \[{{\rm{m}}^2}\].
Hence, the cost of white washing \[1{{\rm{m}}^2} = {\rm{Rs7}}{\rm{.50}}\]
Therefore, the cost of white washing \[74{{\rm{m}}^2}\] \[ = {\rm{Rs}}7.50 \times 74 = {\rm{Rs}}555\]
Then the cost of white washing the walls of the room and the ceiling at the rate of \[{\rm{Rs7}}{\rm{.50}}\] per \[{{\rm{m}}^2}\] is Rs. 555.
Therefore, this is the required answer.
Note:
Here the shape of the room is not given but we will assume it to be a cuboid because the dimensions of the room are given as length, breadth, and height. A cuboid is a three dimensional shape whose sides are rectangular. In real life, rooms are usually in the shape of a cuboid but if in case all the 4 walls and the top and bottom of a room have the same length, breadth, and height, this would mean that it is cubical in shape as a cube has all the sides equal and square shaped. Some other examples of cuboidal figures which we see in our day to day life are matchboxes, shoeboxes, books, etc. All of these have a length, breadth and height respectively.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)