MATH 140
Section 3.8 Related Rates
Calculus
• Related Rates
Related Rates
Fact 1 For each related rates problem, state what you know, what you want, and a formula. These
statements will guide your work for the whole problem.
1. The length of a rectangle is increasing at a rate of 3 cm/s, and its width is decreasing at a rate
of 4 cm/s. When the length is 10 cm and the width is 20 cm, how fast is the area of the rectangle
changing? Is the area growing or shrinking?
2. The volume of a sphere is decreasing at a rate of 4 in3 /s. How fast is the radius decreasing when
the radius is 10 in?
3. A car starts driving North from Preston Idaho at a rate of 20 miles/hr at 12:00. Another car
drives West from Preston at 30 miles per hour at 1:00. At what rate is the distance between the cars
increasing at 2:00?
4. If a snowball melts so that its surface area decreases at a rate of 10 cm2 /hr, find the rate at which
the diameter decreases when the diameter is 8 cm.
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MATH 140
Section 3.8 Related Rates
Calculus
5. Superman is flying horizontally at a height of 200 feet to catch a boulder that is about to crush
Lois Lane. His flight speed is 1000 feet/second. How quickly is the distance from Lois to Superman
changing when the angle of elevation from Lois to Superman is 60◦ ?
Superman
200 ft
60◦
Lois Lane
6. A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the
top and have a height of 1 ft. If the trough is being filled with water at a rate of 12 ft3 /min, how fast
is the water level rising when the water is 6 inches deep?
7. A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How
fast is a rider rising when his seat is 16 m above ground level?
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