Question

When a circle is inscribed into a square, what is the ratio of the area of the circle to the area of the square?

Answer 1

you have to calulate the area of the circle and the square

Answer 2

and using algebra you need to get that rate

Answer 3

so you first say that the area of the square has to be \[a^2\] as its area is side*side, and we take each side as a

Answer 4

and the area of the circle has to be \[\pi r^2=\pi (\frac{ a }{ 2 })^2\]

Answer 5

I see....thank you!

Answer 6

what you have to do to get the rate is divide the area of the circle by the area of the square

Answer 7

you get \[AreaRate=\frac{ \pi (\frac{ a }{ 2 })^2 }{ a^2 }\]

Answer 8

and plug in any number for "a", and solving that would give you the rate

Answer 9

\[\frac{ \pi (\frac{ a }{ 2 })^2 }{ a^2 }=\frac{ \pi \frac{ a^2 }{ 4 } }{ a^2 }=\frac{ \pi a^2 }{ 4a^2 }\]

Answer 10

So the rate would be pi to 4 right?

Answer 11

you eliminate the a^2 as it's multiplying and dividing and you get \[\frac{ \pi }{ 4 }\]

Answer 12

yep, which would be around 0.785

Answer 13

Thank you!

Answer 14

you're welcome!!