Chapter 11

Other Topics in Differential Calculus

Educators

SG

Problem 1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100$\pi$ feet?

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Problem 2

A spherical balloon is inflating at a rate of 27$\pi \mathrm{in}^{3} / \mathrm{sec} .$ How fast is the radius of the balloon increasing when the radius is 3 inches?

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Problem 3

Cars A and B leave a town at the same time. Car A heads due south at a rate of 80 km/hr and car B heads due west at a rate of 60 km/hr. How fast is the distance between the cars increasing after three hours?

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Problem 4

The sides of an equilateral triangle are increasing at the rate of 27 in./sec. How fast is the triangle’s area increasing when the sides of the triangle are each 18 inches long?

SG
Saba G.
Numerade Educator

Problem 5

An inverted conical container has a diameter of 42 inches and a depth of 15 inches. If water is flowing out of the vertex of the container at a rate of $35 \pi \mathrm{in}^{3} / \mathrm{sec},$ how fast is the depth of the water dropping when the height is 5 $\mathrm{in} ?$

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Problem 6

A boat is being pulled toward a dock by a rope attached to its bow through a pulley on the dock 7 feet above the bow. If the rope is hauled in at a rate of 4 ft/sec, how fast is the boat approaching the dock when 25 ft of rope is out?

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Problem 7

A 6-foot-tall woman is walking at the rate of 4 ft/sec away from a street lamp that is 24 ft tall. How fast is the length of her shadow changing?

Kayleah T.
Numerade Educator

Problem 8

The minute hand of a clock is 6 inches long. Starting from noon, how fast is the area of the sector swept out by the minute hand increasing in in. $^{2}/$ min at any instant?

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