If the length of a room is twice its breadth and breadth is twice as long as its height the volume of a room is 512 m3 find the total cost of plastering four walls at the rate of 4.50 per m2
Answers
Let breadth of room be 'M".
Length of a room is twice its breadth.
Length of room = 2M
Breadth is twice as long as its height.
Height of room = M/2
In question we have given that, Volume of room is 512 m³.
We know that, room is cuboid in shape.
So,
Volume of cuboid = length × breadth × height
Substitute the known values in above formula
=> 512 = 2M × M × M/2
=> 512 = M³
=> M = 8
So,
Breadth of room = M
=> 8 m
Length of room = 2M
=> 2(8)
=> 16 m
Height of room = M/2
=> 8/2
=> 4 m
We have to find the area of plastering the four walls.
Formula for the area of four walls :
- Area of base = l × b
- Area of ceiling = l × b
So, Area of four walls = 2(l + b)
Substitute the known values in above formula
=> 2(16 + 8)
=> 2(24)
=> 48 m²
Rate of plastering four walls = 4.50 m²
=> 48 × 4.50
=> Rs. 216
ANSWER:-
Given:
If the length of a room is twice its breadth and breadth is twice as long as it's height the volume of a room is 512m³.
To find:
Find the total cost of plastering four walls at the rate of 4.50 per m².
Solution:
⏺️Let the breadth of a room be 'x'
⏺️The Length of a room is twice is '2x'
⏺️& breadth is twice as long as its height, is x/2
⏺️Volume of a room= 512m³
Therefore,
We know that Formula of volume of cuboid is, (Length×breadth× height).
So,
=) 512 = (2x × x × x/2)
=) 512 = 2x³/2
=) 1024 = 2x³
[512 Multiplied by 2]
=) 2x³ = 1024
=) x³ = 1024/2
[1024 dividing by 2]
=) x³ = 512
=) x= ³√512
[cube of 512]
=) x= 8m
So,
Breadth of room, x= 8m.
Length of room, 2x = 2× 8= 16m.
Height of room, x/2= 8/2 = 4m.
Now,
Area of the 4 walls:
Area of 4 ceiling wall is= 2(l+b)
=) 2(16m+ 8m)
=) 2(24m)
=) 48m
The cost of plastering four walls at the rate of Rs.4.50/m²
=) 48m of the cost of plastering four walls;
=) Rs.(48× 4.50)