Question

At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. The inner edge of the sidewalk is a circle with a radius of 9 m.

Find the exact area of the larger circle
Find the exact area of the smaller circle.
Write an expression to find the exact area of the sidewalk (shaded portion).
Find the approximate area of the sidewalk. Use 3.14 to approximate π.
Answer:
Find the exact area of the larger circle. Show your work. (1 point)
A= N x 11 2 A = n?




Find the exact area of the smaller circle. Show your work. (1 point)
A= n 9 2 A=n?



Write an expression to find the exact area of the sidewalk (shaded portion). Show your work. (2 points) 11 2 – 9 2 x n


Find the approximate area of the sidewalk. Use 3.14 to approximate π. Show your work. (1 point) 11 2 x 3.14 – 9 2 x 3.14=

Answer 1

Well first lets find area of the entire circle itself 

We have the radius be 11.

Pie x radius^2 = A

11 squared is 121.

So we have:

Pie x 121 = area

Pie is 3.14.

The area of the entire circle is exactly 379.94 m.

Now lets put this off to side and solve the inner circle.

Same thing: 

Radius of the inner circle is 9.

Pie x radius^2 = Area

9 squared is 81.

So now:
Pie x 81 = area

Pie is 3.14

3.14 x 81 = exactly 254.34.

The inner pen is exactly 254.34 m

So now knowing :

The whole circle is 379.94
And the inner circle is 254.34

We can subtract the inner circles area from the whole circle and get the area of the outer circle/sidewalk.

379.94 - 254.34 = 125.6

The outer circle/sidewalk is 125.6 m

With this info we can answer your questions.

The exact area of the larger circle is 379.94 m

The exact area of the inner circle is 254.34 m

Expression:
If
Large circle = L
Small circle = S
Sidewalk = W

An expression would be L - S = W

The sidewalk area is exactly 125.6 m

To show your work read what i did above and just show how i did Pie x radius = area.

Hope this helps!
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