Area of 3/4 circle = (3/4)*pi*r^2 = (3/4)*pi*6^2 = 84.82 metres squared
Area of ¼ circle = (1/4)*pi*r^2 = (1/4)*pi*2^2 = 3.142 metres squared
Area of 1/4 circle =(1/4)*pi*r^2 = (1/4)*pi*1^2 = 0.785 metres squared
Total Area = 0.785 + 3.142 + 84.82 = 88.747 m2
TETHERED GOAT- 2
The length of the rope is now increased to 10m. The goat is still tethered at the corner of the barn of 4m by 5m on grassy field.
What is the total area the goat can graze?
Diagram(2)
Everything which is shaded in green is the total area of the grass the goat can eat.
The area shaded in yellow is the part where the goat cannot reach to eat the grass.
5m
4m
ttty
Length of rope is 10m
- Find the equations for the arcs of the circles which bound region (as shaded in diagram 3 below).
Diagram(3) (not drawn to scale)
Q2 has 6 radius
66
Q1 has 5 radius
6
-
Make the origin in the bottom right hand corner of the barn. So the arcs of the circles will have centres (5,0) and (0,4); and arc Q1 has 5m radius and arc Q2 has 6m radius.
Area = ¾ pi* 102 = 235.62m2
Area of red and green quarter circle = ¼* pi* 62 = 28.27m2
Area of blue and green quarter circle = ¼ *pi*52 = 19.635m2
Since we have used the area of green twice. We need to find what is the actual area of this green part.
We know that the green area is approximately a quarter circle of radius 1m. So if we can work the approximate value of the green area, we can then find the total area of the grass the goat can eat.
Total area of lawn eaten by the goat is
= (3/4*pi*102) + (1/4*pi*62) + (1/4*pi*52) – (1/4*pi* 12)
= 235.619449 + 28.27433388 + 19.63495409 – 0.785
= 283.528737 – 0.785
T0TAL AREA = 282.74m2
