{"@context":"https://schema.org/","@type":"Quiz","name":"

What is the length of one side of a square that has the same area as a circle with radius 2 ?

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What is the length of one side of a square that has the same area as a circle with radius 2 ?

","comment":{"@type":"Comment","text":"

Choice C is correct. The area A of a circle with radius $r$ is given by the formula $A=\\pi^{2}$. Thus, a circle with radius $2$ has area $\\pi(2^{2})$, which can be rewritten as $4 \\pi$. The area of a square with side length $s$ is given by the formula $A=s^{2}$. Thus, if a square has the same area as a circle with radius $2$, then $s^{2}=4\\pi$. Since the side length of a square must be a positive number, taking the square root of both sides of $s^{2}=4\\pi$ gives $s=\\sqrt{4\\pi}$. Using the properties of square roots, $\\sqrt{4\\pi}$ can be rewritten as $(\\sqrt{4})(\\sqrt{\\pi})$, which is equivalent to $2\\sqrt{\\pi}$. Therefore, $s=2\\sqrt{\\pi}$.

Choice A is incorrect. The side length of the square isn't equal to the radius of the circle. Choices B and D are incorrect and may result from incorrectly simplifying the expression $\\sqrt{4\\pi}$.

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What is the length of one side of a square that has the same area as a circle with radius 2 ?

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"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$\\sqrt{2\\pi}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$2\\pi$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$2\\sqrt{\\pi}$

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