Question

i didnot under stand the question ?
need help
Gas is escaping a spherical balloon at the rate of 4 cm3 per minute. How fast is the surface area of the balloon shrinking when the radius of the balloon is 24 cm?
Given volume of sphere is V = 4/3 πr^3and the surface area S = 4πr^2.

Answer 1

V = (4/3)π r^3
dV/dt = 4π r^2 dr/dt
-4 = 4π r^2 dr/dt (-4 because V is decreasing)
dr/dt = -1/(πr^2)

S = 4π r^2
dS/dt = 8πr dr/dt
= 8πr(-1/(π r^2) = -8/r

so when r = 24 , dS/st = -8/24 = -1/3

The surface area is decreasing at 1/3 cm^2 per minute

Answer 2

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