Assertion (A): If the radius of a circle grows at a constant rate, its area grows at a constant rate too.
Reason (R): $\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$ .

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 D

Correct answer: D

R is the chain rule applied to $A = \pi r^2$ . True.
A is false: by R, $\frac{dA}{dt}$ grows with $r$ , so the area grows faster and faster.

Concept: Rates and the chain rule
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsRate of change of a quantity

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Assertion (A): If the radius of a circle grows at a constant rate, its area grows at a constant rate too.Reason (R): dAdt=2πrdrdt\frac{dA}{dt} = 2\pi r\frac{dr}{dt}dtdA​=2πrdtdr​.

Explanation

Assertion (A): If the radius of a circle grows at a constant rate, its area grows at a constant rate too.
Reason (R): $\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$ .