Question

13. The length, breadth and height of a classrooom are 6m, 4m, 5m respectively. The length,
breadth of a door are 3m, 2m respectively. Two windows of length 2m and breadth Im are
there. The four walls are to be painted internally with the rate of Rs. 15/sq.m. Find he cost
of painting the classroom
​

Answer 1

Solution :-

The length, breath and height of the classroom are 6m, 4m and 5m

Therefore,

Area of 4 walls = 2( l + b)h

Subsitute the required values,

Area of 4 walls

= 2( 6 + 4)5

= 2( 10 ) 5

= 20 * 5

= 100m²

Now,

We have to find the Area of door and window

Therefore,

Area of door = Length * Breath

Area of door = 3 * 2 = 6m²

Area of 2 windows = 2 * length * breath

Area of 2 windows = 2 * 2 * 1 = 4m²

Now,

Total Area to be painted

= Area of 4 walls - Area of door - Area of 2 windows

Subsitute the required values,

= 100 - 6 - 4

= 100 - 10

= 90m²

Cost of painting 1 m² area = Rs 15

Therefore,

Total cost of painting

= 15 * 90 = Rs 1350 $.$

Answer 2

$\Large{\bold{\mathfrak{\underline{\underline{Given \: information:-}}}}}$

• $\bf{length\: of \: classroom \: = \: 6m }$
• $\bf{breadth \: of \: classroom \: = \: 4m}$
• $\bf{Height \: of \: classroom \: = \: 5m}$
• $\bf{breadth \: of \: a \: door \: = \: 2m \: and \: 3m}$
• $\bf{length \: of \: window \: = \: 2m}$
• $\bf{breadth \: of \: window \: = \: 1m}$
• $\bf{Rate \: of \: four \: walls \: to \: be \: painted \: internally \: = \: 15sq.m}$

$\Large{\bold{\mathfrak{\underline{\underline{What's \: the \: need \: to \: find?}}}}}$

• $\bf{cost \: of \: painting \: the \: classroom.}$

$\Large{\bold{\mathfrak{\underline{\underline{Formulas \: needed \: to \: solve \: this \: question:-}}}}}$

• $\leadsto {\boxed {\bold{Area \: of \: rectangle \: = \: length \: \times \: breadth}}}$
• $\leadsto {\boxed {\bold{Area \: of \: cuboid\: = \: 2(length + breadth) \times height}}}$
• $\leadsto {\boxed {\bold{2 \times length \: \times breadth}}}$

$\Large{\bold{\mathfrak{\underline{\underline{Step \: by \: step \: explaination:-}}}}}$

___________

$\frak{\large\bold {\underbrace{Understanding \: the \: question \: and \: solving \: way}}}$

»» Here first we have to calculate the area of four walls that is by using the formula of area of cuboid. Then in the same way calculating the area of door by using the formula of area of rectangle. Then we would calculate the area of two walls.

»» After that we would calculate the the total area which had been painted by subtracting the areas calculated above and multiply it with the cost that had been taken for painting an area of 1m².

_____________

Let's solve it now!!

Here finding out the area of 4 walls of the room by using the given formula of cuboid.

• $: \implies \: \bf{Area \: of \: cuboid \: = \: 2(length + breadth)}$

Or

• $: \implies \: \bf{Area \: of \: 4 \: walls \: = \: 2(l + b)h}$
• $: \implies \: \bf{Area \: of \: 4 \: walls \: = \: 2(6 +4 )5}$
• $: \implies \: \bf{Area \: of \: 4 \: walls \: = \: 2 \: \times \: 10 \: \times 5}$
• $: \implies \: \bf{Area \: of \: 4 \: walls \: = \: 2 \: \times \:50}$
• $: \implies \: \bf{Area \: of \: 4 \: walls \: = \: 100m {}^{2} }$

Here now we are finding out the area of door by using the given formula of area of rectangle~

• $: \implies \: \bf{Area \: of \: rectangle \: = \: length \: \times \: breadth}$

Or

• $: \implies \: \bf{Area \: of \:door \: = \: length \: \times \: breadth}$
• $: \implies \: \bf{Area \: of \:door \: = \: 3m \: \times \: 2m}$
• $: \implies \: \bf{Area \: of \:door \: = \: 6m {}^{2} }$

Here finding out the area of two windows by using the given formula of 2×length×breadth~

• $: \implies \: \bf{Area \: of \: 2 \: windows \: = \: 2 \: \times \: length \: \times \: breadth}$
• $: \implies \: \bf{Area \: of \: 2 \: windows \: = \: 2 \: \times \: 2 \: \times 1}$
• $: \implies \: \bf{Area \: of \: 2 \: windows \: = \: 4 \times \: 1}$
• $: \implies \: \bf{Area \: of \: 2 \: windows \: = \: 4 m {}^{2} }$

At last we came to knew about the area of 2 windows, door and 4 walls. Thus we would be finding out the the total area which had been painted~

• $: \implies \: \bf{Total \: area \: = \: Area \: of \: 4 \: walls \: - \: area \: of \: 2 \: windows \: - \: area \: of \: door}$
• $: \implies \: \bf{Total \: area \: = \: 100m {}^{2} - 6m {}^{2} - 4m {}^{2} }$
• $: \implies \: \bf{Total \: area \: = \: 100m {}^{2} -10m {}^{2} }$

Now time is to calculate the total cost which had been taken. Let's find out as 1m² painting cost is 15 Rs. thus total cost would be as follows:-

• $: \implies \: \bf{1m {}^{2} \: cost \: = 15 }$
• $: \implies \: \bf{Total \: cost \: = \: 15 \times 90}$
• $: \implies \: \bf{Total \: cost \: = \:Rs.1350}$

$\Large{\bold{\mathfrak{\underline{\underline{Answer:-}}}}}$

• Cost of painting the classroom is Rs.1350