Find the areavof a circle whose perimeter is equal to the square of sideb11cm
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Let’s say that the circle has a radius of rr and the square has a sidelength of kk. The area of a circle is Ac=πr2Ac=πr2 and for the square Asq=k2Asq=k2. Since the areas are the same, we can use this to express kk in terms of r.r.
πr2=k2⇔πr2=k2⇔
π−−√r=kπr=k
Using this we can compute the perimeter of the square as P=4k=4π−−√rP=4k=4πr. The circumference of a circle is 2πr2πr, we can now compute the ratio as
R=4π√r2πr=2π√
πr2=k2⇔πr2=k2⇔
π−−√r=kπr=k
Using this we can compute the perimeter of the square as P=4k=4π−−√rP=4k=4πr. The circumference of a circle is 2πr2πr, we can now compute the ratio as
R=4π√r2πr=2π√
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