Answered: The volume of a cone is changing and…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter2: Linear Equations

Section: Chapter Questions

Problem 72SGR

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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)

Expert Solution

Step 1

The volume of a cine is given by the formula;

$V = \frac{1}{3} {πr}^{2} h$

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.