Question

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and ceiling at the rate of Rs 7.50 per m^2.​

Answer 1

$\rm{\underline{Given,}}$

• Length (l) of room = 5 m
• Breadth (b) of room = 4 m
• Height (h) of room = 3 m

$\star$It can be observed that four walls and the ceiling of the room are to be white washed.

$\star$Total area to be white washed = Area of walls + Area of ceiling of room

$\large{\rm{= 2lh+2bh+lb}}$

$\large{\rm{=2×5×3+2×4×3+5×4}}$

$\large{\rm{=30+24+20}}$

$\large{\rm{=74}}$

$\sf{Area = 74\:m²}$

• Also,

Cost of white washed per m² area = Rs. 7.50 (given)

Cost of white washed 74 m² = Rs. (74×7.50)

=Rs. 555

Answer 2

Given:-

• Length of the room is 5m.
• Height of the room is 4m.
• Breadth of the room is 3m.⠀⠀

⠀⠀

To Find:-

• Find the cost of whitewashing the walls of the room and ceiling at the rate of Rs.7.50 per m^2.

⠀⠀

Concept:-

• Let's understand the concept first. Concept used here is Total Surface Area(TSA) of a Cuboid and Area of a Rectangle.Substitute the given values in the equation and solve it wisely.

⠀

Formulae Applied:-

• Total Surface Area(TSA) of a Cuboid = 2(lb + bh + hl)
• Area of a Rectangle = l × b

⠀⠀

Solution:-

Given that!

Length of the room = 5m

Height of the room = 4m

Breadth of the room = 3m

Rate of whitewashing = Rs.7.50/m^2

[Note:- We whitewash the four walls and ceiling of a room.So,we should find the Total Surface area of the room and the area not to be whitewashed(base)]

According to the question we have!

Total Surface Area(TSA) of a Cuboid = 2(lb + bh + hl)

⟹ 2(lb + bh + hl)

⟹ 2[(5 × 4) + (4 × 3) + (3 × 5)]

⟹ 2[20 + 12 + 15]

⟹ 2[47]

⟹ 2 × 47

⟹ 94

⟹ 94m^2

Hence,

The Total Surface Area(TSA) of the room is 94m^2.

Now,

Area not be whitewashed is Area of the base.

[Note:- Base of a room/Cuboid is in the shape of a rectangle.So,base is a rectangle.]

Area of a Rectangle = l × b

⟹ l × b

⟹ 5 × 4

⟹ 20

⟹ 20m^2

Hence,

The area not to be whitewashed is 20m^2.

Now,

Area to be whitewashed = Area of the room - Area of the base

⟹ Area of the room - Area of the base

⟹ 94 - 20

⟹ 74

⟹ 74m^2

Hence,

The Area to be whitewashed is 74m^2.

Now,

Cost of whitewashing = Rs.7.50 × Area to be whitewashed

⟹ Rs.7.50 × Area to be whitewashed

⟹ 7.50 × 74

⟹ 555

⟹ Rs.555

Hence,

The cost of whitewashing is Rs.555/m^2.

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