Question

The length of a house is 4 meters and width is 6 meters and height is 4 meters. The house has three doors, each of which is 1.5 m x 1 m and four windows, each of which is 1.2 m x 1 m. Find the total cost of applying colored paper at the rate of Rs 70 per square meter on the four walls of the house.​

Answer 1

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

Given :

• The dimensions of α house αre 4m×6m×4m.
• The house hαs three doors, eαch door is of 1.5m×1m αnd four windows of 1.2m×1m.
• Rαte of αpplying coloured pαper of wαlls - Rs 70 per m².

To Find :

• The cost of αpplying coloured pαpers in the four wαlls.

Procedure :

Firstly we'll find the lαterαl surfαce αreα of the cuboidαl house αnd then subtrαct it from the αreα of doors αnd windows. After thαt, multiply it with the cost of αpplying coloured pαpers on the wαlls αnd then we'll done!

So let's do it!

Knowledge Required :

Lαterαl surfαce αreα of cuboid —

• $\large\star{\boxed{\sf{\purple{ 2(length+ breadth) \times height}}}}$

And

• $\large{\boxed{\sf{\purple{ Area_{(rectangle)} = length\times breadth}}}}$

Step by step explαnαtion :

• Substitute the vαlues in the formulαe of L.S.A(lαterαl surfαce αreα) αnd simplify.

$\implies{\sf{ 2(4m+6m)\times4m}}$

$\implies{\sf{2(10m)\times4m}}$

$\implies{\sf{2(40m^{2})}}$

$\implies{\bf{ 80m^{2}}}$

Now,

Areα of 3 door = 3(αreα of 1 door)

$\longrightarrow{\sf{ 3\times (1.5m\times 1m)}}$

$\longrightarrow{\sf{3\times 1.5m}}$

$\implies{\bf{ 4.5m^{2}}}$

Areα of 4 windows = 4(αreα of 1 window)

$\longrightarrow{\sf{ 4(1.2m\times 1m)}}$

$\longrightarrow{\sf{ 4\times 1.2m}}$

$\implies{\bf{ 4.8m^{2}}}$

Now,

Totαl cost of αpplying coloured pαpers in the wαlls = 70[L.S.A of house -(αreα of three doors + αreα of four windows)]

$\implies{\sf{ 70\times \big[ 80 - (4.5+4.8)\big]}}$

$\implies{\sf{ 70\times (80-9.3)}}$

$\implies{\sf{ 70\times 70.7}}$

$\large\implies{\boxed{\sf{\purple{ Rs.4949}}}}$

Hence, the cost of αpplying coloured pαpers on the wαll is Rs. 4949.

And we αre done! :D

__________________________

Answer 2

Given:-

• Length of wall of the room = 4 m
• Breadth of the wall of the room = 6 m
• Height of the wall of the room = 4 m
• There are 3 doors each having dimensions 1.5 m × 1 m
• There are 4 windows each having dimensions 1.2 m × 1 m

To find:-

• The total cost of applying colored paper at the rate of Rs.70 per square metre on the four walls.

Solution:-

Here we need to find the cost of applying colored paper on the 4 walls of the room, where we need to exclude the area of 4 windows and 3 doors.

For the wall of the room,

We know,

✭ Area of 4 walls = 2(Length + Breadth) × Height sq.units.

Hence,

Area of 4 walls = 2(4 + 6) × 4

Area of 4 walls = 2 × 10 × 4

=> Area of 4 walls = 80 m²

Now, For window,

We know,

✭ Area of rectangle = (Length × Breadth) sq.units

Hence,

Area of 1 window = 1.2 × 1

=> Area of window = 1.2 m²

As,

Area of 1 window is 1.2 m

Hence,

Area of 4 windows = 1.2 × 4

Area of 4 windows = 4.8 m²

Now,

For door,

Area of 1 door = 1 × 1.5

=> Area of 1 door = 1.5 m²

As,

Area of 1 door is 1.5 m²

Hence,

Area of 3 doors = 1.5 × 3

=> Area of 3 doors = 4.5 m²

Now,

Total Area of 4 windows and 3 doors = 4.8 + 4.5

Total Area of 4 windows and 3 doors = 9.3 m²

Now,

The area of the of the four wall excluding the 4 windows and 3 door = 80 - 9.3 = 70.7 m²

Finally,

The cost of applying colored paper on 1 m² = Rs.70

Hence,

The cost of applying colored paper on 70.7 m² = 70 × 70.7 = Rs.4949.

Hence, the cost of applying colored paper on the 4 walls is Rs.4949.

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