Question

The dimensions of a room are 15m×10m×5m. Find the total cost of white-washing all four walls and the ceiling of the room at the rate of ₹100 per m^2.
step by step answer please​

Answer 1

Given :

• Length of the room = 15 m

• Breadth of the room = 10 m

• Height of the room = 5 m

• Cost of white washing the room (per m²) = 100.

To find :

The cost of white washing the four walls.

Solution :

To find the white washing the room , first we have to find the area of four walls and the area of the ceiling.

Area of Four walls :-

Using the formula for 4 walls and substituting the values in it , we get :-

$\underline{:\implies \bf{A = 2(l + b)h}}$

Where :-

• A = Area of four walls.
• l = Length
• b = Breadth
• h = Height

$:\implies \bf{A = 2 \times (15 + 10) \times 5}$

$:\implies \bf{A = 2 \times 25 \times 5}$

$:\implies \bf{A = 10 \times 25}$

$:\implies \bf{A = 250}$

$\boxed{\therefore \bf{A = 250\:m^{2}}}$

Hence, the area of four walls is 250 m².

Area of the ceiling :

Using the formula for area of a rectangle and substituting the values in it , we get:

$\underline{:\implies \bf{A = l \times b}}$

Where :-

• A = Area of ceiling.
• l = Length
• b = Breadth

$:\implies \bf{A = 15 \times 10}$

$:\implies \bf{A = 150}$

$\boxed{\therefore \bf{A = 150\:m^{2}}}$

Hence, the area of the ceiling is 150 m².

Now , area of the room excluding the floor :-

==> Area of Four walls + Area of the ceiling

==> (250 + 150) m²

==> 400 m²

Now , to find the total cost , we have to multiply it by the cost of white washing the room per m².

→ Total cost = Rs. (400 × 100)

→ Total cost = Rs. 40000

Hence, the total cost is Rs. 40000.

Answer 2

Given:

• Length of the Room, l = 15m
• Breadth of the Room, b = 10m
• Height of the Room, h = 5m

Find:

• Total cost of white-washing all four walls and the ceiling at the rate of rs. 100/m²

Solution:

Here,

we, know that

$\underline{\boxed{ \bold{\to Surface \: Area \: of \: 4walls = 2(lb + bh + hl)}}}$

So,

$\bold{\to Surface \: Area = 2(lb + bh + hl) - lb}$

where,

• l = 15m
• b = 10m
• h = 5m

So,

$\bold{\leadsto Surface \: Area= 2(lb + bh + hl) - lb}$

$\bold{\leadsto Surface \: Area= 2 \{(15 \times 10) + (10 \times 5) + (5 \times 15) \} - (15 \times 10)}$

$\bold{\leadsto Surface \: Area= 2 \{(150) + (50) + (75) \} - (150)}$

$\bold{\leadsto Surface \: Area= 2 \{150 + 50 + 75 \} - 150}$

$\bold{\leadsto Surface \: Area= 2 (275) - 150}$

$\bold{\leadsto Surface \: Area = 550- 150}$

$\bold{\leadsto Surface \: Area =400 {m}^{2} }$

Hence, the Surface Area fir white washing will be 400m²

___________________

Now,

Cost of white washing for 1m² = rs. 100

So, Cost of white washing for 400m² = 400 × 100 = rs.40000

_________________

Hence, the cost of white washing the for walls including the ceiling of the given room will be rs. 40000