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In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2ar2. (a) 2 h cm r cm Figure 3 Figure 3 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 to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. Show that the volume of the solid, V, is given by V = 1000ar – ar³ . 5 ii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r gives a maximum.

In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2ar2. (a) 2 h cm r cm Figure 3 Figure 3 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 to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. Show that the volume of the solid, V, is given by V = 1000ar – ar³ . 5 ii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r 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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i just need (iv) and (B)

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Question B5 In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2nr?. (а) 2 h cm r cm Figure 3 Figure 3 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 to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. 5 Show that the volume of the solid, V, is given by V = 1000r iii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r gives a maximum. (b) Use calculus to explain why the curve with equation y = lIn x has a positive gradient for all values of x.
Transcribed Image Text:Question B5 In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2nr?. (а) 2 h cm r cm Figure 3 Figure 3 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 to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. 5 Show that the volume of the solid, V, is given by V = 1000r iii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r gives a maximum. (b) Use calculus to explain why the curve with equation y = lIn x has a positive gradient for all values of x.
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