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Question 10 a) x cm x cm 120 cm Figure 2 90 cm Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. Show that the volume of the tray, V, is given by V = 2x³ - 330x² + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum.

Question 10 a) x cm x cm 120 cm Figure 2 90 cm Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. Show that the volume of the tray, V, is given by V = 2x³ - 330x² + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question 10 a) x cm x cm 120 cm Figure 2 90 cm Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. Show that the volume of the tray, V, is given by V = 2x³ - 330x² + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum.
Transcribed Image Text:Question 10 a) x cm x cm 120 cm Figure 2 90 cm Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. Show that the volume of the tray, V, is given by V = 2x³ - 330x² + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum.
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