Question

3. At the mission museum Mrs. Perez visited over break, there is a pond like the one below that has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 10 m. The inner edge of the sidewalk is a circle with a radius of 8 m.

Answer 1

(a)
`36\pi \ m^2`

(b)
`113.04\ m^2`

Explanation:

(a) Write and simplify an expression for the exact area of the sidewalk.

(b) Find the approximate area of the sidewalk. Use 3.14 to approximate .

(a) The sidewalk area is the difference in the area of outer circle and inner circle.

Use formula
`A=\pi r^2` for the area of the circle:

`A_(outer)=\pi \cdot 10^2=100\pi \ m^2\\ \\A_(inner)=\pi \cdot 8^2=64\pi \ m^2`

The difference is

`A_(Sidewalk)=A_(outer)-A_(inner)=100\pi -64\pi =36\pi \ m^2`

(b) Use approximation
`\pi \approx 3.14,` then

`A_(Sidewalk)\approx 36\cdot 3.14=113.04\ m^2`