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Algebraic Relation A = Tr2 A= Area r= radius e) What is the radius of a circle with area 25t?

User DemaxSH
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1 Answer

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Recalling the formula for the area of a circle:


A=\pi\cdot r^2

Divide both sides of the equation by the constant pi :


(A)/(\pi)=r^2

Take the square root of both sides of the equation and take the positive value of the square root, since r is a length and it is positive:


\sqrt[]{(A)/(\pi)}=\sqrt[]{r^2}=r

Therefore:


r=\sqrt[]{(A)/(\pi)}

Since A=25, then:


r=\sqrt[]{(25)/(\pi)}=\frac{\sqrt[]{25}}{\sqrt[]{\pi}}=\frac{5}{\sqrt[]{\pi}}

Use a calculator to find out the decimal representation of the number 5/sqrt(pi):


r=\frac{5}{\sqrt[]{\pi}}\approx2.821

Therefore, the radius of a circle with area 25 is approximately 2.821.

User Erdogant
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