Question

A spherical balloon is inflating with helium at a rate of 641 it? min How fast is the balloon's radius increasing at the instant the radius is 2 ft? Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. (Type an exact answer, using a as needed.) Differentiate both sides of the equation with respect to t. dv dr dt (Type an exact answer, using a as needed. Type an expression using r as the variable.) at the instant the radius is 2 ft. The balloon's radius is increasing at a rate of (Simplify your answer.)

Answer 1

Gires inflating at a rate balloon is 6417 Ft 3 of min rate of change of volume dv Gati pa min dt Wee Let radius of balloon (2) We know volume of balloons (v) = 4 3 a 4 nr 3 Differentiate on both sides dv dt n 63) du dt 2 m (302) dr dt dr dt = 4102 dr dt at radius (r)=eft 64 = 4062)² dr 64 = 16 de dt dr db Refren E4 balloon's radius is increasing at a rate of salmen dr It =4

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