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= 7…

Question

asked Mar 16, 2022 135k views

1 Answer

Rajagp · Answer 1 · 2022-03-22T08:28:41+0000

Answer:

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