Question

a path bounds a circular lawn at a park. if the inner edge of the path is 132 ft. around, approximate the amount of area of the lawn inside a circular path. Approximate pi as 22/7

Answer 1

We have the following picture

the black line represents the inner edge of the path, so we are told that the length of it is 132 ft. We can see that this coincides with the circunference of this circle. Recall that the formula of the circunference of a circle is

`2\cdot\pi\cdot r`

where r is the radius of the circle. Note that, using the given information we have the following equation

`2\cdot\pi\cdot r=132`

Also, note that we are asked for the area. Recall that the area of the circle woulde be given by the formula

`\pi\cdot r^(2)`

where r is the radius of the circle. Since we don't know the value of r, we should use the previously found equation to find the value of r.

We are told to approximate the value of pi as 22/7. So, we have

`2\cdot\pi\cdot r=132\approx2\cdot(22)/(7)\cdot r`

So, if we multiply both sides by 7 and the divide it by 2, we get

`22\cdot r\approx(7)/(2)\cdot132\text{ = 7}\cdot66\text{ = 462}`

Then by dividing both sides by 22 we get

`r\approx(462)/(22)=21`

So the radius of the circle is about 21 ft.

Now we replace this value in the area formula, so we have

`\pi\cdot r^2\approx(22)/(7)\cdot(21)^2=(22\cdot21\cdot21)/(7)=(22\cdot21\cdot3\cdot7)/(7)=22\cdot21\cdot3=1386`

So the enclosed area is about 1386 squared ft.