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 sphereshaped 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  
Math Team Joined: Jul 2011 From: Texas Posts: 2,820 Thanks: 1464  Quote:
$\dfrac{dV}{dt} = 4\pi r^2 \dfrac{dr}{dt}$ 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 
$\displaystyle 40cm^3/s=4\pi r^2(20cm/s)$ $\displaystyle 2cm^2=4\pi r^2$ $\displaystyle r^2=\frac{1cm^2}{2\pi}$ $\displaystyle r=\frac{1}{\sqrt{2\pi}}cm$? 

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