Question

a circular field has a area of 14400 sq ft
What is the diameter of the field?

Answer 1

Answer:

240/sqrt(pi)

Step-by-step explanation:

We know that the area of a circle is $pi*r^2$, and we also know that the diameter of a circle is equal to $2r$.

Let's first make an equation for this problem.

pi*r^2=14400

Dividing both sides by pi, we get

r^2=14400/pi

Now, taking the square root of both sides gives us

r=120/sqrt(pi)

We are trying to find the diameter, which is twice the size of the radius.

Thus, we multiply the equation by two.

2r=240/sqrt(pi)

Answer 2

The diameter of the considered circular field whose area is of 14400 sq. ft. is evaluated being of 135.4055 ft approximately.

How to find the area of a circle?

Suppose the circle has radius of 'r' units, then, its area is given as:

$A = \pi \times r^2$ sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r = d/2, thus, area can be rewritten as:

$A = \pi \times (\dfrac{d}{2})^2$ sq. units

For this case, we're given that:

The area of the circular field = 14400 sq. ft.

Let there is a circle of diameter 'd' with same size as that of the circular field.

Then 'd' = diameter of the circular field too.

Also, area of the circle = $A = \pi \times (\dfrac{d}{2})^2 = 14400$

From this, we get the value of 'd' as:
$\pi \times (\dfrac{d}{2})^2 = 14400\\\\(\dfrac{d}{2})^2 = \dfrac{14400}{\pi}\\\\\text{Taking positive sq. root on both the sides}\\\\\dfrac{d}{2} = \pm \dfrac{120}{\sqrt{\pi}}$

Since diameter cannot be negative, therefore, we take only the positive sign.

Thus, we get:

$\dfrac{d}{2} = \dfrac{120}{\sqrt{\pi}}\\\\d = \dfrac{240}{\sqrt{\pi}} \approx 135.4055 \: \rm ft$

Thus, the diameter of the considered circular field whose area is of 14400 sq. ft. is evaluated being of 135.4055 ft approximately.

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