A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the instant the radius is 30 cm?

Question

anonymous · Answer

The formula for the volume of a sphere is 4/3*PI*R^3. If the radius is 30 units, the total volume is 4/3*PI*30^3 = 113.097 units^3. 

After one minute, the volume has increased with another 500 units^3, so went up to 113.597 units^3. Adding the 500 units^3 to the balloon will have increased the volume and hence the radius of the balloon a bit further. To find the new radius, apply the same formula with the new volume and find Rnew.= 30.04 cm. 

This increase happened within the timeframe of one minute, so the increase is (30.04 - 30 cm)/1 minute = 0.4 cm/min.

anonymous · Answer

Which would that be?

5/(36pi)cm/min
2/(18pi)cm/min
4/(9pi)cm/min
7/(24pi)cm/min

anonymous · Answer

Hi Mattyice, made a little calculation error in my last line. the outcome should be 0.04 cm/min instead of the 0.4 cm/min I copied. Forgot the 0 behind the comma. Can you calculate your four answers to find which one leads to 0.04 ?

anonymous · Answer

Thanks so much! That's what I did and found 4/(9pi)cm/min is 0.444, and that's the closest of the answers so I was gonna go with that. Is that right?

anonymous · Answer

Haven't calculated the four options (no calculator available here) but you did the right thing. Good luck :-)