Mathematics - Calculus
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14. A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft^3/min. How fast is the diameter of the balloon increasing when the radius is 1 ft?
16. A 17-ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 5 ft/s, how fast will the top of the ladder be moving down the wall when it is 8 ft above the ground?
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The expert examines the rate problem for a spherical balloon inflating. Neat, step-wise solutions are provided.
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14. A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft^3/min. How fast is the diameter of the balloon increasing when the radius is 1 ft?
Data: dV/dt = 3 and r = 1
To find: dD/dt
V = (4/3) r^3
Differentiating with respect to t, we get ...
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