Question

A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.
(a) How fast is the radius of the balloon changing at the instant the radius is 40 centimeters?
___cm/min

(b) How fast is the radius of the balloon changing at the instant the radius is 90 centimeters? _____ cm/min

Answer 1

satelite?

Answer 2

btw salaams saifoo

Answer 3

walaikum salam!

whoz u?

Answer 4

lol i jsut realzied you name and figured u were muslim..im muslim too

Answer 5

can u please help me

Answer 6

Oh, cool.
whts your name?
u from?

Answer 7

hey kre

Answer 8

my anmes aamir im from nyc

Answer 9

Oh cool, amir!

Answer 10

The rate of change of the volume is 900 cc/min, which means that\[\frac{dV}{dt} = 900.\]We are interested in the rate of change of the radius. Since\[V = \frac{4}{3}\pi r^3\]we have\[\frac{d\left(\frac{4}{3}\pi r^3\right)}{dt} = \frac{4}{3}\pi \frac{d r^3}{dt} = \frac{4}{3}\pi 3r^2\frac{dr}{dt} = 900 \Rightarrow \frac{dr}{dt} = \frac{225}{\pi r^2}\]so the rate of change of the radius when r = 40 is\[\frac{dr}{dt}(40) = \frac{225}{1600\pi}.\]

Answer 11

wat about 90cm

Answer 12

\[\frac{dr}{dt}(40) = \frac{225}{1600\pi} = \frac{9}{64\pi}\](I forgot to simplify this one).\[\frac{dr}{dt}(90) = \frac{225}{8100\pi} = \frac{1}{36\pi}.\]

Answer 13

thanks