# calculus

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a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?

• calculus -

v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt
-1.5 = 4pi (16) dr/dt
dr/dt = -1.5/64pi

a = 4pi r^2
da/dt = 8pi r dr/dt
= 8pi (4) (-1.5/64pi)
= -3/4 m^2/min

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