CB.Calc.CHA-3.E: Interpret related rates in applied contexts.

Interpret related rates in applied contexts.

Example Problems

The radius

r(t)

of a cone is decreasing at a rate of

6

inches per minute and the height

h(t)

of the cone is increasing at a rate of

9

inches per minute. At a certain instant

t_0

, the radius is

5

inches and the height is

7

inches.
Find

h'(t_0)

.

The radius

r(t)

of a cone is increasing at a rate of

1

foot per second and the height

h(t)

of the cone is increasing at a rate of

3

feet per second. At a certain instant

t_0

, the radius is

2

feet and the height is

5

feet.
Find the units for

V(t_0)

.

The radius

r(t)

of a cone is increasing at a rate of

3

centimeters per second and the height

h(t)

of the cone is decreasing at a rate of

4

centimeters per second. At a certain instant

t_0

, the radius is

8

centimeters and the height is

10

centimeters.
Find

h'(t_0)

.

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