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

Answer:

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

(b) $113.04\ m^2$

Step-by-step 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

$A_{Sidewalk}\approx 36\cdot 3.14=113.04\ m^2$