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

A right circular cone has a volume of $\\frac{1}{3}\\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?

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A right circular cone has a volume of $\\frac{1}{3}\\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?

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

Choice A is correct. The equation for the volume of a right circular cone is $V=\\dfrac{1}{3}\\pi r^{2}h$. It's given that the volume of the right circular cone is $\\dfrac{1}{3}\\pi$ cubic feet and the height is $9$ feet. Substituting these values for $V$ and $h$, respectively, gives $\\dfrac{1}{3}\\pi=\\dfrac{1}{3}\\pi r^{2}(9)$. Dividing both sides of the equation by $\\dfrac{1}{3}\\pi$ givers $1=r^{2}(9)$. Dividing both sides of the equation by $9$ gives $\\dfrac{1}{9}=r^{2}$. Taking the square root of both sides results in two possible values for the radius, $\\sqrt{\\left(\\dfrac{1}{9}\\right)}$, or $-\\sqrt{\\left(\\dfrac{1}{9}\\right)}$. Since the radius can't have a negative value, that leaves $\\sqrt{\\left(\\dfrac{1}{9}\\right)}$ as the only possibility. Applying the quotient property of square roots, $\\sqrt{\\dfrac{a}{b}}=\\dfrac{\\sqrt{a}}{\\sqrt{b}}$, results in $r=\\dfrac{\\sqrt{1}}{\\sqrt{9}}$, or $r=\\dfrac{1}{3}$

Choices B and C are incorrect and may result from incorrectly evaluating $\\sqrt{\\left(\\dfrac{1}{9}\\right)}$. Choice D is incorrect and may result from solving $r^{2}=9$ instead of $r^{2}=\\dfrac{1}{9}$.

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A right circular cone has a volume of $\\frac{1}{3}\\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?

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

$\\frac{1}{\\sqrt{3}}$

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

$\\sqrt{3}$

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

$3$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$\\frac{1}{3}$

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

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-30"}

A right circular cone has a volume of $\frac{1}{3}\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?