A room is 10.2m long,8.5 m wide and 4.6, m high. It has a door measuring 1.5m×2.6m and a window measuring 2 m× 1.7m.Find the cost of tiling the walls at rate of ₹ 13.50 per sq.m.
Answers
Given data : A room is 10.2m long,8.5 m wide and 4.6m high. It has a door measuring 1.5m × 2.6m and a window measuring 2m × 1.7m.
To find : Find the cost of tiling the walls at rate of Rs. 13.50 per m².
Solution : A/C to given data;
- Length of the room = 10.2 m
- Breadth of the room = 8.5 m
- Height of the room = 4.6 m
Let,
- length of the door = 2.6 m and
- height of the door = 1.5 m
- length of the window = 2 m and
- breadth of the window = 1.7 m
Suppose, the shape of the room is cuboidal and the shape of the door and window is rectangular. door and the window are rectangular.
Firstly, we have to find out, total surface area of the room. Now by formula of the total surface area of the cuboid.
➜ Area of the room = 2(LB + BH + HL)
➜ Area of the room = 2(10.2 * 8.5 + 8.5 * 4.6 + 4.6 * 10.2)
➜ Area of the room = 2(86.7 + 39.1 + 46.92)
➜ Area of the room = 2(125.8 + 46.92)
➜ Area of the room = 2(172.72)
➜ Area of the room = 345.44 m²
Now, {By formula of area of the rectangle}
➜ Area of the door = length * breadth
➜ Area of the door = 2.6 * 1.5
➜ Area of the door = 3.8 m²
similarly;
➜ Area of the window = 2 * 1.7
➜ Area of the window = 3.4 m²
Now, we have to find out, area of walls except area of the door and the window.
➜ Area of the walls = Area of the room - {Area of the door + Area of the window}
➜ Area of the walls = 345.44 - {3.8 + 3.4}
➜ Area of the walls = 345.44 - 7.2
➜ Area of the walls = 338.24 m²
Here, we know that, Cost of tiling is Rs 13.5 per m².
➜ Cost of tiling the walls = Area of the walls * Cost of tiling per m².
➜ Cost of tiling the walls = 338.24 * 13.5
➜ Cost of tiling the walls = Rs 4566.24
Answer : Hence, the cost of tiling the walls is Rs 4566.24.
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10.2m= length
8.5m=width
4.6m=height
10.2m× 4.6m×2 (because 2 of them have same dimension)
8.5×4.6×2
thus if u take 4.6 and 2 in common
it is 18.7×9.2=172.04
172.04×13.50= 2223.99
thus 2223.99 is the answer