The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. in.3/min (b) Find the rate of change of the volume when r = 37 inches. in.3/min

 = 1017.87 in³/min

= 17203.35 in³/min

Step-by-step explanation:

given data

radius r of a sphere is increasing at a rate = 3 inches per minute

 = 3

solution

we know volume of sphere is V =

so  

and when r = 9

so rate of change of the volume will be

rate of change of the volume

 = 1017.87 in³/min

and

when r = 37 inches

so rate of change of the volume will be

rate of change of the volume

= 17203.35 in³/min  

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the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0