struggling... Please show your work. i can understand. thanks The radius of a sp

Question

struggling... Please show your work. i can understand. thanks

The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the surface area changing when the radius is 14 centimeters? Hint: The surface area is S = 4 pi r2. Rate of change of surface area = Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6.5 mi /hr. How rapidly is radius of the spill increasing when the area is 7 mi-? The radius is increasing at mi hr.

Explanation / Answer

A )ds/dt = 8pir*(dr/dt) = 704 cm2

b)Area of circle A = pi*r^2

da/dt = 2pi*r*(dr/dt)

pi*r^2 = 7

r = 7 /root(22)

dr/dt = 6.5/ ( 44/ root(22) ) = 6.5 / (2* root(22) = 0.69296 mi/hr

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