Match each part of the circle x^2 + y^2 = 16 in List I with its area in List II.

Match each part of the circle x^2 + y^2 = 16…

Question 43

MediumOriginal question

Match each part of the circle $x^{2} + y^{2} = 16$ in List I with its area in List II.

List I	List II
A. The part above the $x$ -axis	I. $2\pi$
B. The part in the first quadrant	II. $8\pi$
C. The part in the first quadrant below the line $y = x$	III. $\frac{16\pi}{3} - 4\sqrt{3}$
D. The part to the right of the line $x = 2$	IV. $4\pi$

A-IV, B-II, C-I, D-IIICorrect answerYour answerA-II, B-IV, C-III, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answerA-II, B-IV, C-I, D-IIICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

A is half of $16\pi$ , B a quarter, and the line $y = x$ cuts the quadrant into two equal halves, so C is $2\pi$ .
D: $2\int_2^{4} \sqrt{16 - x^{2}}\,dx = 2\left(4\pi - 2\sqrt{3} - \frac{4\pi}{3}\right) = \frac{16\pi}{3} - 4\sqrt{3}$ .

Worth noting

Swapping A and B confuses the half above the axis with the quarter in the first quadrant.

Concept: Using symmetry
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsCircles

Practise this chapter →

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

Practise this chapter →

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

Question 43

Explanation