The volume of a cone is changing and over time the height of the cone measures 15 cm and decreases at a rate of 0.2 cm / min and the radius of the base measures 10 cm and decreases at a rate of 0.3 cm / min. a) Find the ratio with which the volume of the cone changes in that time b) Interpret the result of part a) Remember that the volume of the cone is (check image for formula)
The volume of a cone is changing and over time the height of the cone measures 15 cm and decreases at a rate of 0.2 cm / min and the radius of the base measures 10 cm and decreases at a rate of 0.3 cm / min. a) Find the ratio with which the volume of the cone changes in that time b) Interpret the result of part a) Remember that the volume of the cone is (check image for formula)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
The volume of a cone is changing and over time the height of the cone measures 15 cm and decreases at a rate of 0.2 cm / min and the radius of the base measures 10 cm and decreases at a rate of 0.3 cm / min.
a) Find the ratio with which the volume of the cone changes in that time
b) Interpret the result of part a)
Remember that the volume of the cone is (check image for formula)
Transcribed Image Text:V = Trh
Expert Solution
Step 1
The volume of a cine is given by the formula;
In the given question the value of both the radius and the height of the cone changes with time. So the rate of change of the volume of the cone will also depend on the rate of change of the height and rate of change of radius of the cone.
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