Question

The length, breadth and height of a room are 10m, 8m and 5m respectively.

Find the cost of white washing the four walls and the ceiling of the room at the

rate of ₹8 per m2​

Answer 1

AnswEr :

• Dimensions of room is 10m, 8m and 5m i.e. length, breadth and height respectively.
• Rate of white washing is ₹8 @ m²
• Find the Cost of white washing the four wall and ceiling of the room.

⋆ Basic Fact : Generally any Room is made of 6 faces i.e. (Cuboidal Shape). 4 Walls, 1 Ceiling and 1 Ground.

Here we have to find the Area of 4 walls and ceiling of Room, for that we can either Subtract Area of Ground Floor from Total Surface Area of Room or, Add Area of Ceiling to the Curved Surface Area of Room.

• Let's Head to the Question Now :

⇒ Required Area = CSA + Area of Ceiling

⇒ Req. Area = [ 2h(l + b) ] + [ l × b ]

⇒ Req. Area = [ 2 × 5 (10 + 8) ] + [ 10 × 8 ]

⇒ Req. Area = [ 10 × 18 ] + 80

⇒ Req. Area = 180 m² + 80 m²

⇒ Required Area = 260 m²

• Cost of white washing of Required Area :

⇒ Cost = Required Area × Rate

⇒ Cost = 260 m² × ₹8

⇒ Cost = ₹2,080

∴ Therefore, Cost of white washing of four walls and ceiling of the room is ₹2,080.

Answer 2

$\huge{\underline{\sf{\red{Answer}}}}$

Cost of whitewashing = ₹2,080

________________________________

Given:

Dimensions of a room

$\implies$ Length = 10m

$\implies$ Breadth = 8m

$\implies$ Height = 5m

Cost of White Washing per unit square of area = ₹8

________________________________

To find

Cost of White Washing ceiling and walls of room

________________________________

ForMula

• LSA Of Cuboid = 2 (bh+ lh) + lb(ceiling area)
• Cost = Rate of Whitewash $\times$ Area to be whitwashed

________________________________

SoluTion:

By Applying the given Information in the Formula we get

$2 \times ( 8 \times 5 + 10 \times 5) + (10 \times 8) \\ \\ \implies 2\times (40+50) + 80 \\ \\ \implies 2 \times (90) + 80 \\ \\ \leadsto 180+80 \\ \\ \leadsto \boxed{260 m^2}$

Now,

For whitewashing this area-

We will apply the 2nd Formula

Cost = $8 \times 260$

$\leadsto{\boxed{Rs2,080}}$

__________________________________