Question

A circular field has an area of about 4,000,000 square yards. Write an equation that

represents the boundary of the field. Let (0, 0) represent the center of the field. Use
A= 7m2 to find r (Round to the nearest whole number).

Answer 1

`x^2 + y^2 = 1273885`

Explanation:

Given

`Area = 4000000`

`(h,k) =(0,0)`

Required

The equation of the circle

First, we calculate the radius of the circle using;

`Area = \pi r^2`

This gives:

`4000000= \pi r^2`

Divide both sides by
`\pi`

`(4000000)/(\pi)= r^2`

Take
`\pi` as 3.14

`(4000000)/(3.14)= r^2`

`1273885.35032= r^2`

Approximate

`1273885= r^2`

Rewrite as:

`r^2 = 1273885`

The equation of the circle is:

`(x - h)^2 + (y - k)^2 = r^2`

Where:

`(h,k) =(0,0)`

`r^2 = 1273885`

So, we have:

`(x - 0)^2 + (y -0)^2 = 1273885`

Open brackets

`x^2 + y^2 = 1273885`

(c) is correct.

The difference in
`x^2 + y^2 = 1273885` and (c) in the question is due to approximation