Problem
Gas is escaping from a spherical balloon at a constant rate of 2 ft3/min. How fast, in ft2/min, is the outer surface area of the balloon shrinking when the radius is 12 ft?
| A. 1/2 | C. 1/3 |
| B. 1/5 | D. 1/4 |
spherical balloon
Problem
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
Problem
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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