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In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ³ and its curved surface area is given by 2². 10 r cm Figure 2 h cm Figure 2 shows a solid which is made up of a cylinder with radius r cm and height h cm. A hemisphere of radius r cm is attached at one end of the cylinder. The total surface area of the solid is 980 cm². Express h in terms of r and hence show that the volume of the solid, V, is given by 5 V = 490r-r³

In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ³ and its curved surface area is given by 2². 10 r cm Figure 2 h cm Figure 2 shows a solid which is made up of a cylinder with radius r cm and height h cm. A hemisphere of radius r cm is attached at one end of the cylinder. The total surface area of the solid is 980 cm². Express h in terms of r and hence show that the volume of the solid, V, is given by 5 V = 490r-r³

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.
Chapter9: Surfaces And Solids
Section9.CR: Review Exercises
Problem 12CR
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Question 9 a) In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ³ and its curved surface area is given by 2². 00 T cm Figure 2 h cm Figure 2 shows a solid which is made up of a cylinder with radius r cm and heighth cm. A hemisphere of radius 7 cm is attached at one end of the cylinder. The total surface area of the solid is 980 cm². Express h in terms of r and hence show that the volume of the solid, V, is given by V = 490gr - b) Use calculus to find the value of r which gives the maximum volume of the solid. c) Use calculus to confirm that your value of r gives a maximum.
Transcribed Image Text:Question 9 a) In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ³ and its curved surface area is given by 2². 00 T cm Figure 2 h cm Figure 2 shows a solid which is made up of a cylinder with radius r cm and heighth cm. A hemisphere of radius 7 cm is attached at one end of the cylinder. The total surface area of the solid is 980 cm². Express h in terms of r and hence show that the volume of the solid, V, is given by V = 490gr - b) Use calculus to find the value of r which gives the maximum volume of the solid. c) Use calculus to confirm that your value of r gives a maximum.
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