For each model, write a fraction greater than 1 for the parts that are shaded.
1 answer:
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Answer:
The change in the volume of a sphere whose radius changes from 40 feet to 40.05 feet is approximately 1005.310 cubic feet.
Step-by-step explanation:
The volume of the sphere (), measured in cubic feet, is represented by the following formula:
Where is the radius of the sphere, measured in feet.
The change in volume is obtained by means of definition of total difference:
The derivative of the volume as a function of radius is:
Then, the change in volume is expanded:
If and
, the change in the volume of the sphere is approximately:
The change in the volume of a sphere whose radius changes from 40 feet to 40.05 feet is approximately 1005.310 cubic feet.