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V = 525лr 2 7ær³ 8 Use calculus to find the value of r which gives the maximum volume, and confirm that your value of r gives a maximum.

V = 525лr 2 7ær³ 8 Use calculus to find the value of r which gives the maximum volume, and confirm that your value of r gives a maximum.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter81: Introduction To Computer Numerical Control (cnc)
Section: Chapter Questions
Problem 4A: A rectangular solid has length L=12.6 mm, width W=23.8 mm, and height H=32.5 mm. Find the length of...
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In this question, you may find the following useful. For a cone of radius r, height h and length of slant edge L, Volume = r²h Curved surface area = πrL rcm y cm Figure 3 r cm Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height r cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. V = The total surface area of the solid, which includes the base, is 525 cm². (b) Find y in terms of r and hence show that the volume of the solid, V, is given by 525лr 7лr³ 2 8 (c) Use calculus to find the value of r which gives the maximum volume, and confirm that your value of r gives a maximum.
Transcribed Image Text:In this question, you may find the following useful. For a cone of radius r, height h and length of slant edge L, Volume = r²h Curved surface area = πrL rcm y cm Figure 3 r cm Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height r cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. V = The total surface area of the solid, which includes the base, is 525 cm². (b) Find y in terms of r and hence show that the volume of the solid, V, is given by 525лr 7лr³ 2 8 (c) Use calculus to find the value of r which gives the maximum volume, and confirm that your value of r gives a maximum.
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