Question

Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm^3/s. How fast is the radius of the balloon increasing when the diameter is 50cm? formula V=4/3(PI)r^3

Answer 1

\[V=(4/3)*\pi*r^3\]
\[dV/dt=4\pi*r^2(dr/dt)\]
\[r=d/2=50/2=25\]
\[100=4\pi*25(dr/dt)\]
\[100=100*\pi(dr/dt)\]
\[1=\pi(dr/dt)\]
\[dr/dt=1/\pi (cm)\]

Answer 2

Woops 1/pi (cm/s)

Answer 3

Did you square the radius?

Answer 4

OHH I forgot.. crap sorry