Answer

Verified

484.2k+ views

Hint:

Find out the area of 4 walls and the ceiling individually. Add them together to get the total area. Then find out the costing for white wash.

Complete step-by-step answer:

Let $ABCD$ is the floor of a room. The length is $AB=CD=5m$ , breadth is $BC=CD=4m$ .

Height is 3m.

Now we have to find out the area of 4 walls.

Let us first find out the area of the wall which is perpendicular to the side $AB$.

For this wall the length is 5 meter, and the breadth is the height which is 3 meter.

We know that the area of a rectangle is = $length\times breadth$

So, the area of the wall which is perpendicular to the side $AB$ is:

$\begin{align}

&=\left( 5\times 3 \right){{m}^{2}} \\

&=15{{m}^{2}} \\

\end{align}$

The area of the wall which is perpendicular to the side $CD$ is basically the same as the area of the wall which is perpendicular to the side$AB$ . The length and the breadth, which is basically the height, are the same for both the walls.

Now the area of the wall which is perpendicular to the side $BC$ is:

$=\left( 4\times 3 \right){{m}^{2}}$

As the length of this wall is 4 meter and the breadth is 3 meter, which is the height.

So, the area is $=(4\times 3)=12{{m}^{2}}$

Similarly, the area of the wall which is perpendicular to the side $AD$ is basically the same as the area of the wall which is perpendicular to the side $BC$ . The length and the breadth, which is basically the height, are the same for both the walls.

Now, the total area of 4 walls is:

$=\left( 2\times 15 \right)+\left( 2\times 12 \right)=30+24=54{{m}^{2}}$

The area of the ceiling is the same as the floor.

So, the area of the ceiling is:

$=\left( 5\times 4 \right){{m}^{2}}=20{{m}^{2}}$

The total area is for white washing = total area of 4 walls + area of ceiling.

$\begin{align}

&=\left( 54+20 \right){{m}^{2}} \\

&=74{{m}^{2}} \\

\end{align}$

Now, the cost of white washing for one square meter is Rs. 7.50

The cost of white washing for 74 square meters is Rs.

$\begin{align}

&=74\times 7.50 \\

&=555 \\

\end{align}$

Therefore we need Rs. 555 to white wash the walls of the room and the ceiling.

Note: Alternatively we can directly use the area of four walls:

$=2\times \left( l+b \right)\times h$ , where $l$ is the length, $b$ is the breadth, $h$ is the height.

If we put the values in this formula:

$\begin{align}

& =2\times (5+4)\times 3=2\times 9\times 3 \\

& =54{{m}^{2}} \\

\end{align}$

So, the area of four walls is 54 square meters.

Find out the area of 4 walls and the ceiling individually. Add them together to get the total area. Then find out the costing for white wash.

Complete step-by-step answer:

Let $ABCD$ is the floor of a room. The length is $AB=CD=5m$ , breadth is $BC=CD=4m$ .

Height is 3m.

Now we have to find out the area of 4 walls.

Let us first find out the area of the wall which is perpendicular to the side $AB$.

For this wall the length is 5 meter, and the breadth is the height which is 3 meter.

We know that the area of a rectangle is = $length\times breadth$

So, the area of the wall which is perpendicular to the side $AB$ is:

$\begin{align}

&=\left( 5\times 3 \right){{m}^{2}} \\

&=15{{m}^{2}} \\

\end{align}$

The area of the wall which is perpendicular to the side $CD$ is basically the same as the area of the wall which is perpendicular to the side$AB$ . The length and the breadth, which is basically the height, are the same for both the walls.

Now the area of the wall which is perpendicular to the side $BC$ is:

$=\left( 4\times 3 \right){{m}^{2}}$

As the length of this wall is 4 meter and the breadth is 3 meter, which is the height.

So, the area is $=(4\times 3)=12{{m}^{2}}$

Similarly, the area of the wall which is perpendicular to the side $AD$ is basically the same as the area of the wall which is perpendicular to the side $BC$ . The length and the breadth, which is basically the height, are the same for both the walls.

Now, the total area of 4 walls is:

$=\left( 2\times 15 \right)+\left( 2\times 12 \right)=30+24=54{{m}^{2}}$

The area of the ceiling is the same as the floor.

So, the area of the ceiling is:

$=\left( 5\times 4 \right){{m}^{2}}=20{{m}^{2}}$

The total area is for white washing = total area of 4 walls + area of ceiling.

$\begin{align}

&=\left( 54+20 \right){{m}^{2}} \\

&=74{{m}^{2}} \\

\end{align}$

Now, the cost of white washing for one square meter is Rs. 7.50

The cost of white washing for 74 square meters is Rs.

$\begin{align}

&=74\times 7.50 \\

&=555 \\

\end{align}$

Therefore we need Rs. 555 to white wash the walls of the room and the ceiling.

Note: Alternatively we can directly use the area of four walls:

$=2\times \left( l+b \right)\times h$ , where $l$ is the length, $b$ is the breadth, $h$ is the height.

If we put the values in this formula:

$\begin{align}

& =2\times (5+4)\times 3=2\times 9\times 3 \\

& =54{{m}^{2}} \\

\end{align}$

So, the area of four walls is 54 square meters.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE