SOLUTION: the volume of a sphere is a function of the radius of the sphere.
write a function for the volume of a ball.evalutae the function for a volleyball of radius 10.5cm
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-> SOLUTION: the volume of a sphere is a function of the radius of the sphere.
write a function for the volume of a ball.evalutae the function for a volleyball of radius 10.5cm
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Question 218254: the volume of a sphere is a function of the radius of the sphere.
write a function for the volume of a ball.evalutae the function for a volleyball of radius 10.5cm Answer by solver91311(24713) (Show Source):
Assume a circular disk of infinitesimal thickness of radius , the -axis through the center and normal to the surface of the disk. Also assume a stack of such disks going from to , the radius of each disk being equal to the -coordinate of the point of intersection of the disk and the plane. The radius of the approximate hemisphere so described is related to the coordinates of each such point of intersection by the following:
1.
The incremental volume (that is the volume of any one of the disks) is the cross-sectional area of the disk times its thickness, so:
2.
And the approximate volume of the hemisphere is then the sum of all of the incremental volumes:
3.
In the limit, as decreases without bound, the volume of the hemisphere is equal to:
4.
Substituting from 1:
5.
This can be evaluated:
6.
Since this is a function of giving the volume of a hemisphere, multiply by 2 to get the volume of the entire sphere:
Substitute 10.5 and do the arithmetic to get the volume of your volleyball. Since the measurement of the radius was given to the nearest 1/10th, you should roundoff and present your answer to the nearest 1/10th as well. The result of any calculation involving measurements cannot be more precise than the least precise of the measurements.
