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valkas [14]
3 years ago
6

A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of

the circle. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fractin in terms of Pie.

Mathematics
1 answer:
krek1111 [17]3 years ago
5 0

Answer:

Step-by-step explanation:

it is given that Square contains a chord of of the circle equal to the radius thus from diagram

QR=chord =radius =R

If Chord is equal to radius then triangle PQR is an equilateral Triangle

Thus QO=\frac{R}{2}=RO

In triangle PQO applying Pythagoras theorem

(PQ)^2=(PO)^2+(QO)^2

PO=\sqrt{(PQ)^2-(QO)^2}

PO=\sqrt{R^2-\frac{R^2}{4}}

PO=\frac{\sqrt{3}}{2}R

Thus length of Side of square =2PO=\sqrt{3}R

Area of square=(\sqrt{3}R)^2=3R^2

Area of Circle=\pi R^2

Ratio of square to the circle=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }

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Answer:

Part 1: Already solved.

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Now that we have the first quartile, we need to find the third quartile. Since the median was actually the first "1" in the data set, the third quartile will be the median of the numbers to the right of that "1": 1, 1, 5/4, 2, 2. Cross out the leftmost two numbers, and cross out the rightmost two numbers. We are left with a third quartile of 5/4.

Now that we have both the third and first quartiles, we can find the interquartile range! The IQR is calculated by finding the third quartile minus the first quartile. 5/4 - 1/4 = 4/4 = 1.

So, your interquartile range is 1 quesadilla.

Hope this helps!

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