A tin has a fitting cylindrical lid which overlaps its cylindrical body by 5 cm. When completely closed, it has base radius x cm and height y cm, as shown in the diagram. The body and the lid are made from thin metal sheet such that the difference in their radii is negligible. The total area of metal sheet used to make the tin and its lid is 400z cm². 5 cm y cm x cm Show that the volume V cm³ of the tin is given by V = Tx(200–x² – 5x). If x varies, find by differentiation the values of x and y for which V has its maximum value. 20 55 [x = = y = 3
A tin has a fitting cylindrical lid which overlaps its cylindrical body by 5 cm. When completely closed, it has base radius x cm and height y cm, as shown in the diagram. The body and the lid are made from thin metal sheet such that the difference in their radii is negligible. The total area of metal sheet used to make the tin and its lid is 400z cm². 5 cm y cm x cm Show that the volume V cm³ of the tin is given by V = Tx(200–x² – 5x). If x varies, find by differentiation the values of x and y for which V has its maximum value. 20 55 [x = = y = 3
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 46E
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Transcribed Image Text:A tin has a fitting cylindrical lid which overlaps its cylindrical body by 5 cm. When
completely closed, it has base radius x cm and height y cm, as shown in the diagram. The
body and the lid are made from thin metal sheet such that the difference in their radii is
negligible. The total area of metal sheet used to make the tin and its lid is 400r cm?.
) cm
' cm
Y cm
Show that the volume V cm of the tin is given by V = Ax(200-x² - 5x).
If x varies, find by differentiation the values of x and y for which V has its maximum value.
20
55
[x =
, y=-
3
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