The area of the largest circle that fits inside a square with 4 sides is?

Question

Please help!

Answer 1

Let side of square = x
radius of circle = x / 2
Area of circle = π (x / 2) ² = π x ² / 4

Answer 2

Ok. Since we don't know how big the square is, we'll consider each side to be x units long.

Thus, the radius of the largest circle to fit inside the square is half the length of one side. Why? The circle will share the same center point and will share a single point with each of the four sides of the square.

So, remember that the area of a circle is equal to pi times the radius squared. In this case, r = x/2 so A = pi(x/2)^2 = (pi x^2)/4.

Answer 3

Let s=length of side of square
Since for circles A=pi*r^2,
the diameter of a circle is twice the radius,
and the circle has to fit inside the square of length s,
the area of the largest circle that fits inside a square with length s is:
pi*(d/2)^2 = pi*(s/2)^2 =

....s^2.......s^2
pi.-----.=.pi.-----
....2^2.........4

So it's pi times ( divided by 4)

I know 61 digits of pi, btw. It's 3.14159265358897932384626433832795028841971693993751058209749945...
(but you dont need that many :)

Answer 4

I thought about this for a few minutes then you can see this: draw a line from the center of each side of the square forming and X the draw your circle inside of your square. Your diameter (length across the circle) cannot exceed the length across from 1 side to other of the square.. Thank you! Calculate diameter: C = pi(d)

Answer 5

If x = length of side of the square, then it is also the diameter of the largest circle.
Hence area of the largest circle will be
(π/4) x^2.

Answer 6

Just a point for the young'ns who think this is worthless. I did too a gizzillion years ago. But unless your career involves the question "do you want fries with that?" you DO use this kind of thing all the time....art (including graphic art - as in web design, video game design, etc.), landscaping, carpentry are just some of the areas that don't fall into the geeky engineering, math professor categories (I can say that because I have been an injunear for 30 years).

Given some of the horrendous answers I've seen in this math section of Answers, I'm really impressed with this group...everyone seems to have gotten it correct - well those who give a s**t.

Answer 7

If the length of one side of the square is L
Then the radius of the circle = L/2 (draw this if you are not sure about this)

So the area = πr² = π(L/2)² = πL²/4

Answer 8

Let us take side of square as x.
then radius of the circle is equal to x/2
Area of a circle is pi*r^2
pi (x/2)^2
pi x^2/4
So the area of the circle is (x^2)pi/4

Answer 9

the diameter of the circle with the largest area is equal
to the side of the square
area of the circle=pi*(d^2)/4=pi*s^2/4 where s=side of the square

Answer 10

let s = measure of the square's side

then.
A = pi*(s^2)/4 square units------(ans.)