Question

Could someone please help me?? I'm stuck.

A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the area of the circle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square. (3 points) Show ALL work.

Answer 1

@ParthKohli @TuringTest Help?

Answer 2

@ash2326

Answer 3

Let's first draw a figure
Assume that the circle is touching all the sides

Answer 4

Okay, what comes next?

Answer 5

Let the side of square be a
That's also the diameter of circle
What's the are of a square?

Answer 6

A=s^2 ?

Answer 7

What's the side of square here? use that in the formula

Answer 8

A=a^2?

Answer 9

Good, now what's the radius of circle?

Answer 10

Ummm, is it A=pi*a^2?

Answer 11

a is the diameter, so a/2 will be the radius. Now use the formula

Answer 12

I'm sorry, I'm not sure how to do that.... I'm very bad with this sort of questions.

Answer 13

No problem, I'll explain you.
For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square.
Square side is a
Diameter of circle will be a
Radius=(diameter)/2
\[r=\frac a 2\]
Area of circle=\(\pi\times r^2\)
\[Area\ of\ circle=\pi\times \frac {a^2}{4}\]
Do you get this ?

Answer 14

Kinda sorta.... Still very confused/:

Answer 15

Where do you have doubt?

Answer 16

More like, I don't know where to go from here.

Answer 17

Ratio of area of square to circle
It's easy divide area of square by circle

Answer 18

Can you take me through it step by step because I'm still not sure how to do that.....

Answer 19

\[\large \text{Ratio}=\frac{\text{Area of square}}{\text{Area of circle}}=\frac{a^2}{\pi \times \frac {a^2}{4}}\]

Answer 20

Ok, and where do I go from here?

Answer 21

Cancel the common terms
\[\large \text{Ratio}=\frac{\text{Area of square}}{\text{Area of circle}}=\frac{\cancel {a^2}}{\pi \times \frac {\cancel{a^2}}{4}}=\frac 4 \pi\]

Answer 22

Ok, what comes next?

Answer 23

It's over

Answer 24

Oh! Oh brother.. You see how bad I am at these. Thank you so much