A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm, as shown. The radii of the tin and the lid are both x cm. The tin and the lid are made from the thin metal film with an area of 80r cm² and there is no wastage. The volume of the tin film is V cm? . xcm ↑ Icm Lid xcm Tin Now complete the following questions: a. Show that V = r(40x – x² – x³). Given that x varies: b. Use differentiation to find the positive value of x for which V is stationary. c. Prove that this value of x gives a maximum value of V. d. Find this maximum value of V. e. Determine the percentage of the metal sheet used in the lid when Vis a maximum.
A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm, as shown. The radii of the tin and the lid are both x cm. The tin and the lid are made from the thin metal film with an area of 80r cm² and there is no wastage. The volume of the tin film is V cm? . xcm ↑ Icm Lid xcm Tin Now complete the following questions: a. Show that V = r(40x – x² – x³). Given that x varies: b. Use differentiation to find the positive value of x for which V is stationary. c. Prove that this value of x gives a maximum value of V. d. Find this maximum value of V. e. Determine the percentage of the metal sheet used in the lid when Vis a maximum.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm, as shown. The radii of the tin and the lid are both x cm. The tin and the lid are made from the thin
metal film with an area of 80r cm? and there is no wastage. The volume of the tin film is V cm.
xcm
I Icm
Lid
xcm
Tin
Now complete the following questions:
a. Show that V = x(40x – x2 - x').
Given that x varies:
b. Use differentiation to find the positive value of x for which V is stationary.
c. Prove that this value of x gives a maximum value of V.
d. Find this maximum value of V,
e. Determine the percentage of the metal sheet used in the lid when Vis a maximum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1c03b12-59a6-4a4a-af4b-1894cd77ac88%2F359b3ec3-9740-4f32-aa65-b3ccf3f2ea8a%2Fd92m92_processed.png&w=3840&q=75)
Transcribed Image Text:A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm, as shown. The radii of the tin and the lid are both x cm. The tin and the lid are made from the thin
metal film with an area of 80r cm? and there is no wastage. The volume of the tin film is V cm.
xcm
I Icm
Lid
xcm
Tin
Now complete the following questions:
a. Show that V = x(40x – x2 - x').
Given that x varies:
b. Use differentiation to find the positive value of x for which V is stationary.
c. Prove that this value of x gives a maximum value of V.
d. Find this maximum value of V,
e. Determine the percentage of the metal sheet used in the lid when Vis a maximum.
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