spherical balloon

Volume of Inflating Spherical Balloon as a Function of Time

A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume V of the balloon as a function of time t (in seconds). Hint: Use composite function relationship Vsphere = 4/3 πr3 as a function of x (radius), and x (radius) as a function of t (time).

A.   V(t) = 5/2 πt3 C.   V(t) = 9/2 πt3
B.   V(t) = 7/2 πt3 D.   V(t) = 3/2 πt3


Rate of change of surface area of sphere

Gas is escaping from a spherical balloon at the rate of 2 cm3/min. Find the rate at which the surface area is decreasing, in cm2/min, when the radius is 8 cm..

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