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straightbarz4643
24.07.2020 •
Mathematics
Approximate the change in the volume of a sphere when its radius changes from r = 40 ft to r equals 40.05 ft (Upper V (r )equals four thirds pi r cubed ). When r changes from 40 ft to 40.05 ft, Upper DeltaValmost equals nothing ftcubed.
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Ответ:
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.
Ответ:
1,12
Step-by-step explanation: