For the circle x^2 + y^2 = 20, which of the following statements are true? I. Its radius is 2√(5). II. ∫_-2√(5)^2√(5) √(20 - x^2) dx = 10π. III. The area it encloses is 4∫₀^20 √(20 - x^2) dx. IV. Its part in the second quadrant has area 5π.

Question 44

MediumOriginal question

For the circle $x^{2} + y^{2} = 20$ , which of the following statements are true?
I. Its radius is $2\sqrt{5}$ .
II. $\int_{-2\sqrt{5}}^{2\sqrt{5}} \sqrt{20 - x^{2}}\,dx = 10\pi$ .
III. The area it encloses is $4\int_0^{20} \sqrt{20 - x^{2}}\,dx$ .
IV. Its part in the second quadrant has area $5\pi$ .

I, II and IV onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerI and II onlyCorrect answerYour answerII and IV onlyCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

I: $r^{2} = 20$ , so $r = 2\sqrt{5}$ . II: the integral is the half above the $x$ -axis, $\frac{20\pi}{2} = 10\pi$ .
III is false: the upper limit must be the radius $2\sqrt{5}$ , not 20. IV: each quadrant is $\frac{20\pi}{4} = 5\pi$ .

Worth noting

Taking III as true puts the limit at 20, the right side of the equation, instead of the radius $2\sqrt{5}$ .

Concept: Area of a region of a circle
Typical timeTypical: 120 s
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The rule this testsCircles

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