Question

The length, breadth and height of a bungalow are 8m, 6m, 7m respectively. The length, breadth of door are 5m, 4m respectively. Two windows of length 4m and breadth 1m are there. The four walls are to be painted internally with the rate of 20 sq.m. Find the cost of painting the bungalow.​

Answer 1

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

• $\leadsto \bf{Length \: of \: bungalow \: = \: 8m}$
• $\leadsto \bf{Breadth \: of \: bungalow \: = \: 6m}$
• $\leadsto \bf{Breadth \: of \: bungalow \: = \: 7m}$
• $\leadsto \bf{Length \: of \: door \: = \: 5m}$
• $\leadsto \bf{Breadth \: of \: door \: = \: 4m}$
• $\leadsto \bf{Length \: of \: window \: = \: 4m}$
• $\leadsto \bf{Breadth \: of \: window \: = \: 1m}$

$\bold{\Large{ \underline {\underline{\mathfrak{Need \: to \: be \: calculated:-}}}}}$

• $\leadsto \bf{Cost \: of \: painting \: the \: bungalow \: ?}$

$\bold{\Large{ \underline {\underline{\mathfrak{Usage \: of \: formulas:-}}}}}$

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

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

_________

$\bf \large \underbrace{Understanding \: the \: question \: and \: solving \: method}$

$\red \bigstar$ Here first we have to calculate the area of four walls of the bungalow 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 four walls of bungalow by applying the formula of cuboid.

$\red \bigstar$ After that we would calculate the total area which had been painted of the bungalow by subtracting the areas calculated above and multiply it with the cost that had been taken for painting an area of 1m² that is 20sq.m.

_________

$\bold{\Large{ \underline {\underline{\mathfrak{Here \: are \: the \: calculations :-}}}}}$

$\blue \bigstar$ Here we finding out the area of 4 walls of the room by using the given formula of cuboid.

• ➛ Area of cuboid = 2(length+breadth)

Evaluation of values:

• ➛ Area of 4walls = 2(l+b)h
• ➛ Area of 4walls = 2(8+6) 7
• ➛ Area of 4walls = 2 × 14 × 7
• ➛ Area of 4walls = 28 × 7
• ➛ Area of 4walls = 196 m²

$\blue \bigstar$ Here now we are finding out the area of door by using the given formula of area of rectangle

• ➛ Area of door = length × breadth

Substituting values:

• ➛ Area of door= 5 × 4
• ➛ Area of door= 20m²

$\blue \bigstar$Here finding out the area of two windows by using the given formula of 2×length×breadth.

• ➛ Area of 2 windows = 2 × length × breadth

Substituting values:

• ➛ Area of 2 windows = 2 × 4 × 1
• ➛ Area of 2 windows = 2 × 4
• ➛ Area of 2 windows = 8m²

$\blue \bigstar$ 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 by subtracting all of them.

• ➛ Total area = Area of4 walls −area of 2 windows − area of door

Where,

• ➛ Area of 4walls= 196 m²
• ➛ Area of door= 20m²
• ➛ Area of 2 windows = 8m²

Substituting values:

• ➛ Total area = 196m² - 20m² - 8m²
• ➛Total area = 168m²

$\blue \bigstar$ Now time is to calculate the total cost which had been taken. Let's find out as 1m² painting cost is 20 Rs. thus total cost would be as follows:-

• ➛ Total cost = 168 × 20
• ➛ Total cost = Rs.3360

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

• $\boxed{ \bf {{Cost \: of \: painting \: the \: bungalow \: is \: Rs.3360}}}$

$\bold{\Large{ \underline {\underline{\mathfrak{Know \: more:-}}}}}$

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