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March 17th, 2018, 05:58 PM   #1
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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 17th, 2018 at 11:57 PM.
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March 17th, 2018, 06:16 PM   #2
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Originally Posted by Monox D. I-Fly View Post
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 $r$
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March 18th, 2018, 01:50 AM   #3
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$\displaystyle 40cm^3/s=4\pi r^2(20cm/s)$
$\displaystyle 2cm^2=4\pi r^2$
$\displaystyle r^2=\frac{1cm^2}{2\pi}$
$\displaystyle r=\frac{1}{\sqrt{2\pi}}cm$?
Thanks from skeeter
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