Assertion (A): The area enclosed by the circle x^2 + y^2 = 12 is 12π square units. Reason (R): The radius of the circle x^2 + y^2 = 12 is 12.

Question 35

EasyOriginal question

Assertion (A): The area enclosed by the circle $x^{2} + y^{2} = 12$ is $12\pi$ square units.
Reason (R): The radius of the circle $x^{2} + y^{2} = 12$ is 12.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The radius is $\sqrt{12} = 2\sqrt{3}$ , not 12, so R is false.
$4\int_0^{2\sqrt{3}} \sqrt{12 - x^{2}}\,dx = \pi\left(2\sqrt{3}\right)^{2} = 12\pi$ , so A is true.

Worth noting

A radius of 12 would give $144\pi$ ; A holds because the right side 12 is the square of the radius.

Concept: Area of a region of a circle
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsCircles

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Assertion (A): The area enclosed by the circle x2+y2=12x^{2} + y^{2} = 12x2+y2=12 is 12π12\pi12π square units.Reason (R): The radius of the circle x2+y2=12x^{2} + y^{2} = 12x2+y2=12 is 12.

Explanation

Assertion (A): The area enclosed by the circle $x^{2} + y^{2} = 12$ is $12\pi$ square units.
Reason (R): The radius of the circle $x^{2} + y^{2} = 12$ is 12.