The volume V of a right circular cone of radius r and height h is given by V = 1 3 π r 2 h . Suppose that the height decreases from 50 cm to 49.64 cm and the radius increases from 10 cm to 10.15 cm . Compare the change in volume of the cone with an approximation of this change using a total differential.
The volume V of a right circular cone of radius r and height h is given by V = 1 3 π r 2 h . Suppose that the height decreases from 50 cm to 49.64 cm and the radius increases from 10 cm to 10.15 cm . Compare the change in volume of the cone with an approximation of this change using a total differential.
Solution Summary: The author compares the change in volume V of a right circular cone with its radius and height.
The volume
V
of a right circular cone of radius
r
and height
h
is given by
V
=
1
3
π
r
2
h
. Suppose that the height decreases from
50
cm
to
49.64
cm
and the radius increases from
10
cm
to
10.15
cm
. Compare the change in volume of the cone with an approximation of this change using a total differential.
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY