How fast is the balloon's radius growing when…

How fast is the balloon's radius growing when the radius is 10 cm?

Question 16

MediumOriginal question

Air is pumped into a spherical balloon at a steady 100 cm³ every second. For a sphere of radius $r$ , $V = \frac{4}{3}\pi r^{3}$ and the surface area is $S = 4\pi r^{2}$ .

How fast is the balloon's radius growing when the radius is 10 cm?

\frac{1}{4 \pi}

cm/sCorrect answerYour answer

\frac{1}{2 \pi}

cm/sCorrect answerYour answer

\frac{1}{\pi}

cm/sCorrect answerYour answer

\frac{2}{\pi}

cm/sCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$100 = 4\pi(100)\frac{dr}{dt}$ .
$\frac{dr}{dt} = \frac{1}{4\pi}$ cm/s.

Worth noting

$\frac{1}{2\pi}$ halves the rate for twice the radius; the rate goes as $\frac{1}{r^{2}}$ , so it falls to a quarter.

Concept: Related rates at a new instant
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsRate of change of a quantity

Practise this chapter →

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

Practise this chapter →

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

How fast is the balloon's radius growing when the radius is 10 cm?

Question 16

Explanation