Read the two statements and choose the correct option.
I. If the radius of a sphere grows at a constant rate, its volume also grows at a constant rate.
II. If the foot of a ladder leaning on a wall slides away at a constant speed, its top slides down at a constant speed.

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

I is false: $\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}$ grows as $r$ grows.
II is false: from $x^{2} + y^{2} = l^{2}$ , $\frac{dy}{dt} = -\frac{x}{y}\frac{dx}{dt}$ , which changes as $x$ grows and $y$ shrinks.

Worth noting

A steady rate in one quantity gives a steady rate in another only when the two are linked linearly, as a radius and a circumference are.

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Read the two statements and choose the correct option.I. If the radius of a sphere grows at a constant rate, its volume also grows at a constant rate.II. If the foot of a ladder leaning on a wall slides away at a constant speed, its top slides down at a constant speed.