Question

9. The dimensions of a room are (9 m X8 m X 6.5 m). It has one door
of dimensions (2 mx1.5 m) and two windows, each of dimensions
(1.5 m X 1 m). Find the cost of whitewashing the walls at * 25 per
square metre.​

Answer 1

$\large\underline{\sf{Given- }}$

The dimensions of a room are (9 m X8 m X 6.5 m).

It has one door of dimensions (2 mx1.5 m).

It has two windows, each of dimensions (1.5 m X 1 m).

$\large\underline{\sf{To\:Find - }}$

Tje cost of whitewashing the walls at ₹ 25 per m²

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\red{\boxed{ \bf{ \: Area_{(4 \: walls)} = 2(l \: + \: b)h}}}$

where

• l represents the length of room

• b represents the breadth of room

• h represents the height of room

$\red{\boxed{ \bf{ \: Area_{(rectangle)} = length \times breadth}}}$

$\large\underline{\sf{Solution-}}$

Dimensions of room

Length of room, l = 9 m

Breadth of room, b = 8 m

Height of room, h = 6.5 m

So,

$\rm :\longmapsto\: \: Area_{(4 \: walls)} = 2(l \: + \: b)h$

$\rm \: = \: \:2 \times (9 + 8) \times 6.5$

$\rm \: = \: \:2 \times 17 \times 6.5$

$\rm \: = \: \:17 \times 13$

$\rm \: = \: \:221 \: {m}^{2}$

Thus,

$\red{\boxed{ \bf{ \: Area_{(4 \: walls)} = 221 \: {m}^{2}}}}$

Now,

Dimensions of window.

Length of window, l = 1.5 m

Breadth of window, b = 1 m

So,

$\rm :\longmapsto\:Area_{(window)} \: = \: 1 \times 1.5$

$\rm \: = \: \:1.5 \: {m}^{2}$

So,

$\red{\boxed{ \bf{ \: Area_{(2 \: windows)} = 3 \: {m}^{2} }}}$

Dimensions of door

Length of door, l = 2 m

Breadth of door, b = 1.5 m

So,

$\rm :\longmapsto\:Area_{(door)} = 2 \times 1.5$

$\rm \: = \: \:3 \: {m}^{2}$

So,

$\red{\boxed{ \bf{ \: Area_{(door)} = 3 \: {m}^{2} }}}$

Now,

Area to be white - wash

$\rm \: = \: \:Area_{(4 \: walls)} - Area_{(2 \: windows)} - Area_{(door)}$

$\rm \: = \: \:221 - 3 - 3$

$\rm \: = \: \:221 - 6$

$\rm \: = \: \:215 \: {m}^{2}$

Now,

According to statement,

Cost of white - washing the walls 1 m² is ₹ 25

So,

Cost of white - washing 215 m² = 215 × 25 = ₹ 5375

Additional Information :-

$\red{\boxed{ \bf{ \: Area_{(square)} = {side}^{2}}}}$

$\red{\boxed{ \bf{ \: Area_{(rhombus)} = base \times height}}}$

$\red{\boxed{ \bf{ \: Area_{(parallelogram)} = base \times height}}}$

$\red{\boxed{ \bf{ \: Area_{(circle)} = \pi \: {r}^{2}}}}$