Read the two statements and choose the correct option.
I. The area enclosed by $x^{2} + y^{2} = 4$ is twice the area enclosed by $x^{2} + y^{2} = 2$ .
II. The part of $x^{2} + y^{2} = 4$ in the first quadrant has the same area as the whole circle $x^{2} + y^{2} = 1$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I: the right sides are the squares of the radii, so the areas are $4\pi$ and $2\pi$ . True.
II: $\int_0^{2} \sqrt{4 - x^{2}}\,dx = \frac{4\pi}{4} = \pi$ , the area of a circle of radius 1. True.

Worth noting

Doubting I reads 4 and 2 as the radii; they are the squares of the radii, so the areas are in the ratio $4 : 2$ .

Ten questions from Area of Bounded Regions, at your own pace.

Explanation