Cheap paper cups A cone-shaped paper drinking cup is to hold 100 cubic centimeters of water (about 4 ozs). Find the height and radius of the cup that will require the least amount of paper. The volume of such a cup is given by the volume of a cone formula: V = (1/3)ar²h, and the area of the paper is given by for formula for surface area of a cone A = Tr/r + h?. (a)What Julia function relates h and r through the constraint on the volume? Oh(r) h(r) (1/3) * pi *r^2 100/(1/3 * pi * r^2) = 100 * (1/3) * pi * r 2 %3D %3D h(r) (b) What Julia function would correctly represent A (r)? OA(r) A(r) pi * r * sqrt (r^2 + h^2) pi * r * sqrt (r^2 + h(r)^2) pi * r * sqrt (r^2) OA(r) (c) Based on your answers above, what value of r minimizes A (r) (d) What is the value of h for this value of r?
Cheap paper cups A cone-shaped paper drinking cup is to hold 100 cubic centimeters of water (about 4 ozs). Find the height and radius of the cup that will require the least amount of paper. The volume of such a cup is given by the volume of a cone formula: V = (1/3)ar²h, and the area of the paper is given by for formula for surface area of a cone A = Tr/r + h?. (a)What Julia function relates h and r through the constraint on the volume? Oh(r) h(r) (1/3) * pi *r^2 100/(1/3 * pi * r^2) = 100 * (1/3) * pi * r 2 %3D %3D h(r) (b) What Julia function would correctly represent A (r)? OA(r) A(r) pi * r * sqrt (r^2 + h^2) pi * r * sqrt (r^2 + h(r)^2) pi * r * sqrt (r^2) OA(r) (c) Based on your answers above, what value of r minimizes A (r) (d) What is the value of h for this value of r?
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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Question
Transcribed Image Text:Cheap paper cups
A cone-shaped paper drinking cup is to hold 100 cubic centimeters of
water (about 4 ozs). Find the height and radius of the cup that will require
the least amount of paper.
The volume of such a cup is given by the volume of a cone formula:
V = (1/3)Tr²h,
and the area of the paper is given by for formula for surface area of a cone
A = Tr/r2 + h².
(a)What Julia function relates h and r through the constraint on the
volume?
Oh(r)
h(r)
(1/3) * pi * r^2
100/ (1/3 * pi * r^2)
= 100 * (1/3) * pi * r^2
Oh(r)
(b) What Julia function would correctly represent A (r)?
OA(r)
A(r) = pi * r * sqrt (r^2 + h(r)^2)
OA(r)
pi * r * sqrt (r^2 + h^2)
%3D
pi *r * sqrt (r^2)
(c) Based on your answers above, what value of r minimizes A (r)
(d) What is the value of h for this value of r?
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