Question

A circular flower bed is 19 m in diameter and has a circular sidewalk around it that is 2 m wide. Find the area of the sidewalk in square meters. Use 3.14 for pi.

The area of the sidewalk is ____ m^2

Answer 1

We can model the problem as two concentric circles.
We want to find the area between the circles.
The equation for the area of the sidewalk is:
A = pi * (R ^ 2 - r ^ 2)
Where,
R: greater radio
r: minor radius
We have then:
R = 19/2 + 2
R = 11.5 m
On the other hand,
r = 19/2
r = 9.5 m
Substituting values we have:
A = 3.14 * ((11.5) ^ 2 - (9.5) ^ 2)
A = 131.88 m ^ 2
Answer:
The area of the sidewalk in square meters is:
A = 131.88 m ^ 2

Answer 2

The area of the sidewalk is 131.88 sq. m.

First find the area of the bed with the sidewalk. Since the sidewalk is all around the circle, this will increase the diameter by 4 m, making d=23. The area of the circle is given by

A=πr²

The radius would be 23/2 = 11.5:
A=3.14(11.5)² = 415.265

Now find the area of the flower bed without the sidewalk. Since d=19, r=19/2=9.5:
A=3.14(9.5²) = 283.385

Subtract the two:
415.265-283.385 = 131.88