Question

A room is 9m long, 8m broad and 6.5m high. It had one door of dimensions 2m × 1.5m and three windows each dimensions 1.5m × 1m. Find the cost of white washing the wall at Rs.3.80 per sq. metre.​

Answer 1

Answer:

Rs. 811.30

Step-by-step explanation:

Given Length of a room = 9 m

Breadth of a room = 8 m

Height of a room = 6.5 m

Area of 4 walls = 2(1 + b) h

= 2 (9 m + 8 m) x 6.5 m

= 2 x 17 m x 6.5 m

= 221 m²

Length of a door = 2m

Breadth of a door = 1.5 m

Area of a door = Length x Breadth

= 2 m x 1.5 m

= 3 m²

Length of a window = 1.5 m

Breadth of a window = 1 m

Since, area of one window = Length x Breadth

= 1.5 m x 1 m

= 1.5 m²

Thus, Area of 3 such windows = 3 x 1.5 m²

= 4.5 m²

Area to be white washed = Area of 4 walls – (Area of one door + Area of 3 windows)

Area to be white washed = [221 – (3 + 4.5)] m²

= (221 – 7.5) m²

= 213.5 m²

We have cost of white washing for 1 m² area = Rs. 3.80

Cost of white washing for 213.5 m² area = Rs. (213.5 x 3.80)

= Rs. 811.30

Answer 2

Question :

A room is 9m long, 8m broad and 6.5m high. It had one door of dimensions 2m × 1.5m and three windows each dimensions 1.5m × 1m. Find the cost of white washing the wall at Rs.3.80 per sq. metre.

Answer :

$\sf\pink{Given:}$

For Room :

• length of room is 9 m.

• breadth of room is 8 m.

• height of room is 6.5 m.

For door :

• length of door is 2 m.

• breadth of door is 1.5 m.

For Windows :

• There are three windows .

• length of window is 1.5 m.

• breadth of window is 1 m.

Rate :

• Rate of white washing is Rs 3.80 m²

$\sf\pink{To\:find:}$

• cost of white washing walls .

Explanation :

To find the cost of white washing we need to find the lateral surface area of the room that is the surface area of its walls and then subtract the are of one door and three windows to get the actual area of the walls and then multiply it by the rate of white washing .

$\sf\purple{Lateral\:surface\:area = 2 ( l + b ) h }$

$\longrightarrow\sf{ 2\times ( 9 + 8)\times 6.5}$

$\longrightarrow\sf{ 2\times 17\times 6.5}$

$\longrightarrow\sf{ 34\times 6.5}$

$\longrightarrow\sf{ 221}$

Therefore the lateral surface are or the area of four walls including the area of one door and three window is 221 m²

$\sf\purple{area\:of\:door = l\times b }$

$\longrightarrow\sf{2\times 1.5}$

$\longrightarrow\sf{3}$

Therefore the area of the door is 3 m².

$\sf\purple{area\:of\:3\:Windows = 3\times (l\times b) }$

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

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

$\longrightarrow\sf{4.5 }$

Therefore the area of 3 windows is 4.5 m².

Actual Area of walls = Lateral surface area - ( area of door + area of three windows )

$\longrightarrow\sf{221 - (3 + 4.5)}$

$\longrightarrow\sf{221 - 7.5}$

$\longrightarrow\sf{213.5}$

Therefore the area of walls is 213.5 m²

$\sf\purple{cost\:of\:white\: Washing = Area\times rate }$

$\longrightarrow\sf{213.5\times 3.80}$

$\longrightarrow\sf{811.3}$

• Therefore the cost is Rs 811.3