My Math Forum [ASK] Balloon Being Blown

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 March 17th, 2018, 06:58 PM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry [ASK] Balloon Being Blown Icha is going to blow a sphere-shaped rubber balloon. She uses a pump to infuse the air with the volume addition rate $\displaystyle 40cm^3/s$. If the radius addition rate is 20 cm/s, the radius of the sphere after being blown is .... A. $\displaystyle \frac{1}{\sqrt\pi}$ cm B. $\displaystyle \frac{1}{\sqrt{2\pi}}$ cm C. $\displaystyle \frac{1}{2\sqrt\pi}$ cm D. $\displaystyle \frac{1}{3\sqrt\pi}$ cm E. $\displaystyle \pi$ cm Please give me some hints. Thanks. Last edited by skipjack; March 18th, 2018 at 12:57 AM.
March 17th, 2018, 07:16 PM   #2
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Quote:
 Originally Posted by Monox D. I-Fly Icha is going to blow a sphere-shaped rubber balloon. She uses a pump to infuse the air with the volume addition rate $\displaystyle 40cm^3/s$. If the radius addition rate is 20 cm/s, the radius of the sphere after being blown is .... A. $\displaystyle \frac{1}{\sqrt\pi}$ cm B. $\displaystyle \frac{1}{\sqrt{2\pi}}$ cm C. $\displaystyle \frac{1}{2\sqrt\pi}$ cm D. $\displaystyle \frac{1}{3\sqrt\pi}$ cm E. $\displaystyle \pi$ cm Please give me some hints. Thanks.
$\dfrac{d}{dt}\left(V = \dfrac{4}{3}\pi r^3\right)$

$\dfrac{dV}{dt} = 4\pi r^2 \dfrac{dr}{dt}$

substitute your given values and determine $r$

 March 18th, 2018, 02:50 AM #3 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry $\displaystyle 40cm^3/s=4\pi r^2(20cm/s)$ $\displaystyle 2cm^2=4\pi r^2$ $\displaystyle r^2=\frac{1cm^2}{2\pi}$ $\displaystyle r=\frac{1}{\sqrt{2\pi}}cm$? Thanks from skeeter

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