A A rectonqular sheet ot alum:inum has perimeter. 36 ft and dimensicns x ft by yft. The sheet 13 to be rolled' into the shape of a circular cylınder having Circumference x ft Determine the that will) maximize the of the as shown. values of' x and y volume circular cylinder. a) write an equation for the per r imeter of the sheet in terms x and y . b) Determine a formula for the volume of the cylinder that depends on on ly x. (ス= 2r-) c) Analyze the derivative of the volume function to determine the dimenslons of eylinder having maximum valume.
A A rectonqular sheet ot alum:inum has perimeter. 36 ft and dimensicns x ft by yft. The sheet 13 to be rolled' into the shape of a circular cylınder having Circumference x ft Determine the that will) maximize the of the as shown. values of' x and y volume circular cylinder. a) write an equation for the per r imeter of the sheet in terms x and y . b) Determine a formula for the volume of the cylinder that depends on on ly x. (ス= 2r-) c) Analyze the derivative of the volume function to determine the dimenslons of eylinder having maximum valume.
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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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
Determine values of x and y for a cylinder. See image.
Transcribed Image Text:A
A rectonqular sheet of alumınum
has perimeter. 36 ft and dimensicns
x ft by y ft. The sheet
1ô to be rolled' into the shape
of a
circumference x ft
Determine the
that wil) maximize
of the eircular cylnder.
circular cylinder having
as shown.
values of x and y
the
volume
a) write
On equation for the
per
rimeter of the sheet in
terms
x and y.
b) Determine a formula for the
volume of the eylinder that
depends on on ly x..
(メ= 2rr)
c) Analyze the derivative of
the volume function to determine
the dimensions of eylinder
having maximum valume.
Transcribed Image Text:Circumference = x ft
%3D
- x ft-
y ft
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