# calculus

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a splenical ballon is being inflated @ 10 cubic inches per secound. how fast is the radius of the ballon increasing when the surface area of the ballon is 2 pi square inches( answer to 4 decimal places)?

• calculus -

I once had a splenical balloon. It was almost spherical.

With that in mind,

v = 4/3 pi r^3
dv/dt = 4 pi r^2 dr/dt

so, plug and chug

10 = 2 pi dr/dt
dr/dt = 10/2pi = 1.5915 in/s

Note: surface area is 4pi r^2

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