In the diagram, point P is a point of tangency. Find the radius r of circle O.
1 answer:
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Answer:
a) see below
b) 40x20 meters
Step-by-step explanation:
Write down what you know:
- The area of the enclosure is length*width, so
- The length of the fencing is 80 meters, so
Now we have to combine these two equations above, and get rid of y in the process.
First rewrite the second as:
Then substitute for y in the first:
b) To maximize A, find the zero of the first derivative:
So y = (80-40)/2 = 20 meters.
Answer:
Area = 733 m² (to the nearest meter)
Step-by-step explanation:
<u></u>
<u>Formulae</u>
- Circumference of a circle = 2
r
- Area of a circle =
(where r is the radius of the circle)
<u>Find the radius</u>
circumference = 96 m
Using the circumference of a circle formula:
⇒ 2r = 96
⇒ r = 96 ÷ 2 = 48
⇒ r = 48 ÷ = 48/
<u>Find the area</u>
radius r = 48/
Using the area of a circle formula:
⇒ A = r²
⇒ A = (48/
)²
⇒ A = 2304/
⇒ A = 733.3859778...
⇒ A = 733 m² (to the nearest meter)