What is the diameter of a circle that contains 7500 square feet?

Answer 1

The area of a circle is equal to pi times the square of it's radius.

The diameter is equal to twice the radius

We can say then:

a = π(d / 2)2

∴ d = 2(a / π)1/2

We can then plug in the given area of the circle (7500f2, where f is a foot) to get it's diameter:

d = 2(7500f2 / π)1/2

d = 100f × (3 / π)1/2

d ≈ 97.72 feet

Now we can check our answer by plugging this value in to the original equation we used for area:

a = π(d / 2)2

∴ a ≈ π(97.72f / 2)2

∴ a ≈ π(48.86f)2

∴ a ≈ π × 2387.2996 f2

∴ a ≈ 7499.9 f2

Which brings us back to our original value with loss of accuracy due to rounding, showing that we are indeed correct.