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cm y cm Figure 3 Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height ro cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. r cm 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 V = 525πτ 2 7πr² 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.

cm y cm Figure 3 Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height ro cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. r cm 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 V = 525πτ 2 7πr² 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.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter84: Binary Numeration System
Section: Chapter Questions
Problem 5A
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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, r²h Curved surface area = TrL Volume = rcm y cm Figure 3 Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height 2 cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. r cm The total surface area of the solid, which includes the base, is 525π cm². (b) Find y in terms of r and hence show that the volume of the solid, V, is given by V = 525лr 2 7πr² 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, r²h Curved surface area = TrL Volume = rcm y cm Figure 3 Figure 3 shows a cylinder of radius r cm and height y cm. A cone of radius r cm and height 2 cm is attached to the cylinder at one end. (a) Find the length of slant edge of the cone in terms of r. r cm The total surface area of the solid, which includes the base, is 525π cm². (b) Find y in terms of r and hence show that the volume of the solid, V, is given by V = 525лr 2 7πr² 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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