"A spherical balloon is to be deflated so that its radius is decreases at a constant rate of 15 cm/min. At what rate must air be removed when the radius is 9 cm?" I know how to calculate the volume of a sphere, but I'm stuck in setting this up and solving it. Any help is appreciated.
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dr/dt = -15 cm/min
Volume of a sphere = (4/3) pi r^3
dV/dt = (4/3) pi (3r^2) dr/dt
dV/dt = 4 pi r^2 dr/dt
dV/dt = 4 pi (9)^2 (-15)
dV/dt = -4,860 pi cm^3/min
Air must be removed at a rate of 4860 cm^3/min when the radius = 9.
Volume of a sphere = (4/3) pi r^3
dV/dt = (4/3) pi (3r^2) dr/dt
dV/dt = 4 pi r^2 dr/dt
dV/dt = 4 pi (9)^2 (-15)
dV/dt = -4,860 pi cm^3/min
Air must be removed at a rate of 4860 cm^3/min when the radius = 9.