2. In this problem, you will find the dimensions of the right circular cone of minimal volume which circumscribes a sphere of radius 3". Refer to the diagram below when answering the questions which follow. |AB| (a) Explain why |AC| |ED| |EC| h D 3 reflect ACDE about CE and rotate A r B work to express V as a function of the variable x alone. - Simplify your expression for V as much as possible. C (b) Rewrite the equality from (a) in terms of the variables x and r. (c) Solve your equation from (b) for the variable r. (d) Use the fact that the volume V of the cone is: V = r²h and your previous E3D X (e) Use the properties of the derivative to minimize the volume of the cone. Then indicate the dimensions of r and h for the minimal cone.
2. In this problem, you will find the dimensions of the right circular cone of minimal volume which circumscribes a sphere of radius 3". Refer to the diagram below when answering the questions which follow. |AB| (a) Explain why |AC| |ED| |EC| h D 3 reflect ACDE about CE and rotate A r B work to express V as a function of the variable x alone. - Simplify your expression for V as much as possible. C (b) Rewrite the equality from (a) in terms of the variables x and r. (c) Solve your equation from (b) for the variable r. (d) Use the fact that the volume V of the cone is: V = r²h and your previous E3D X (e) Use the properties of the derivative to minimize the volume of the cone. Then indicate the dimensions of r and h for the minimal cone.
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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Transcribed Image Text:2. In this problem, you will find the dimensions of the right circular cone of minimal volume
which circumscribes a sphere of radius 3". Refer to the diagram below when answering
the questions which follow.
C
| AB | |ED|
|EC|
h
X
reflect
ACDE about CE
and rotate
Ar
ΦΕ
B
work to express V as a function of the variable x alone.
- Simplify your expression for V as much as possible.
C
(a) Explain why |AC|
(b) Rewrite the equality from (a) in terms of the variables x and r.
(c) Solve your equation from (b) for the variable r.
(d) Use the fact that the volume V of the cone is: V = r²h and your previous
E 3D
X
(e) Use the properties of the derivative to minimize the volume of the cone. Then
indicate the dimensions of r and h for the minimal cone.
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