a circle is inscribed in a square of side s. write the area of the circle as a function of s?

Question

i am having trouble understanding this question
the area of a circle is pie r^2
how would you right it if it had to be written in regards to the squares side??

Answer 1

The side of the square is the diameter of the circle.
The radius would be half of that, so:
Pi (s/2)^2

Answer 2

Tricky.

So the circle is inscribed in a square. That would mean it is inside of it. I recommend drawing a picture to help yourself.

We don't want to do too much work. So lets draw a picture:

[O]

Pretend for a few moments that this is the thing you're talking about.

[O] |

Notice above: The side of the square, when you move it over a little bit, can also be the diameter of the circle!

So you know:

d = s

To get the radius, divide s by 1/2.

r = 1/2s

Now that you have the radius, plug 1/2s into the equation.

a = 1/4s^2 * pi

So the area is one fourth s squared times pi, in written form.

Answer 3

a = pir^2 the place r is the radius. In our case the circle is inscribed in a sqaure with factors s. because of the fact the circle is inscribed it touches the sq. in 4 places and it relatively is on the midpoints of the two factors. This factor interested in the middle of the circle is the radius. So via inspection we are able to state that the radius is s/2 and substitute this into our equation above and get a = pi(s/2)^2 = a million/4pis^2

Answer 4

Because each side of the square touches the circle at only one point (tangent point) which is half way down the length of that side of the square.

When you draw a line from any those four points to the center of the circle, you get the radius of the circle, which is exactly one half the side of the square.

Therefore the Area of circle = Pi x radius^2 = Pi x (Side/2)^2

Answer 5

A circle inscribed in a square has a diameter equal to the length of the sides of the square. Thus, if s is the length of the sides of the square, the radius of the circle is s/2. Hence, the area of the circle is

A = П(s/2)^2
A = (П/4)s^2

Answer 6

The diamer of the circle is the same as the side of the square, which is 's.'
The radius of the circle is s/2.
Area PI r^2, where r=s/2
=PI s^2/4