Part C (Rectangular Cake Tins): Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square from each corner. The sides of the rectangular tinplate are in a ratio p:q. (а) Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your process and findings from Part B, determine the exact value of x that gives the maximum volume for this cake tin. (b) Repeat this process for a rectangular tinplate in the ratio 3:1. (c) Explore rectangular tinplate with sides in at least two other ratios. Hint: Change the value of both p and q, and determine exact solutions for x.
Part C (Rectangular Cake Tins): Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square from each corner. The sides of the rectangular tinplate are in a ratio p:q. (а) Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your process and findings from Part B, determine the exact value of x that gives the maximum volume for this cake tin. (b) Repeat this process for a rectangular tinplate in the ratio 3:1. (c) Explore rectangular tinplate with sides in at least two other ratios. Hint: Change the value of both p and q, and determine exact solutions for x.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.2: Perimeter And Area Of Polygons
Problem 31E: Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are...
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part c , question b, c and d please
Transcribed Image Text:Part C (Rectangular Cake Tins):
Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square
from each corner. The sides of the rectangular tinplate are in a ratio p:q.
(а)
Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your
process and findings from Part B, determine the exact value of x that gives the maximum volume for
this cake tin.
(b)
Repeat this process for a rectangular tinplate in the ratio 3:1.
(c)
Explore rectangular tinplate with sides in at least two other ratios.
Hint: Change the value of both p and q, and determine exact solutions for x.
(d)
Develop a conjecture about the relationship between x (the cut to be made for the square) and the
length of each side of the rectangle tinplate (p and q) such that the cake tin has a maximum volume.
Show sufficient working to support your conjecture.
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