A rectangular flower bed has a perimeter of 96m, and its length is twice its breadth. The flower bed is surrounded by a concrete path of witdth 40 cm and height 15 cm. Calculate the volume of concrete used for the path, giving your answer in meter cubic.
width --- w
length --- 3w
2(w+3w) = 96
4w = 48
w = 12 m or 1200 cm
3w = 36 m or 3600 cm
area of flower bed = 1200(3600) cm^2
area of rectangle including path
= (1280)(3680) cm^2
area of walkway = the difference or 390400 cm^2
volume of concrete needed for walk
= 390400(15) cm^3
= 5,856,000 cm^3
= appr 5.9 cubic metres
check my arithmetic
To calculate the volume of concrete used for the path, we first need to determine the dimensions of the rectangular flower bed.
Let's assume the breadth of the flower bed is 'b' meters. Since the length of the flower bed is twice its breadth, the length can be expressed as '2b' meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + breadth)
In this case, the perimeter is given as 96m, so we can write the equation as:
96 = 2(2b + b)
Simplifying the equation:
96 = 2(3b)
48 = 3b
b = 16
So, the breadth of the flower bed is 16 meters, and the length would be 2 * 16 = 32 meters.
Now, let's calculate the dimensions of the outer rectangle formed by the path.
Width of the concrete path = 40 cm = 0.4 m
Height of the concrete path = 15 cm = 0.15 m
The outer length of the path would be the length of the flower bed plus twice the width of the path.
Outer length = 32 + 2(0.4) = 32.8 m
The outer breadth of the path would be the breadth of the flower bed plus twice the width of the path.
Outer breadth = 16 + 2(0.4) = 17.8 m
To calculate the volume of concrete used for the path, we multiply the length, breadth, and height of the path.
Volume = Outer length * Outer breadth * Height
Volume = 32.8 * 17.8 * 0.15 = 93.096 m³
Therefore, the volume of concrete used for the path is 93.096 cubic meters.