Solution Found!
Volume The radius r and height h of a right circular cone
Chapter 3, Problem 14E(choose chapter or problem)
Problem 14E
Volume The radius r and height h of a right circular cone are related to the cone’s volume V by the equation
a. How is dV/dt related to dh/dt if r is constant?
b. How is dV/dt related to dh/dt if h is constant?
c. How is dV/dt related to dh/dt and if neither r nor h is constant?
Questions & Answers
QUESTION:
Problem 14E
Volume The radius r and height h of a right circular cone are related to the cone’s volume V by the equation
a. How is dV/dt related to dh/dt if r is constant?
b. How is dV/dt related to dh/dt if h is constant?
c. How is dV/dt related to dh/dt and if neither r nor h is constant?
ANSWER:
Solution
Step 1 of 1
Here volume of the circular cone is given as
(a) Now if r is constant it means only height is changing
So ,
Differentiating both sides, we get
Thus the relation is