   Chapter 3.7, Problem 32E

Chapter
Section
Textbook Problem

# A right circular cylinder is inscribed in a cone with height h and base radius r . Find the largest possible volume of such a cylinder.

To determine

To find:

The largest possible volume of a cylinder inscribed in a cone with height h and base radius r.

Explanation

1) Concept:

First derivative test:

Suppose c is a critical number of a continuous function f defined on an interval.

(a) If f'(x)>0 for all x<c and f'(x)<0 for all x>c, then f(c) is the absolute maximum value of f.

(b) If f'(x)<0 for all x<c and f'(x)>0 for all x>c, then f(c) is the absolute minimum value of f.

2) Formula:

Volume of right circular cylinder=V=πr2h

Where, r=radius and h=height of right circular cylinder

3) Given:

A right circular cylinder is inscribed in a cone of height h and base radius r.

4) Calculation:

Volume of right circular cylinder=V=πr2h

Where, r=radius and h=height of right circular cylinder

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