Questions & Answers

Question

Answers

Answer

Verified

147.6k+ 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.

Students Also Read