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(b) i. Use calculus to find the value of r which gives the minimum surface area of the solid. ii. Confirm that your value of r gives a minimum. (c) If the height of the solid with the minimum surface area is H cm, write down H the value of giving your answer in its simplest form.

(b) i. Use calculus to find the value of r which gives the minimum surface area of the solid. ii. Confirm that your value of r gives a minimum. (c) If the height of the solid with the minimum surface area is H cm, write down H the value of giving your answer in its simplest form.

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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(b) i. Use calculus to find the value of r which gives the minimum surface area of the solid. ii. Confirm that your value of r gives a minimum. (c) If the height of the solid with the minimum surface area is H cm, write down H the value of giving your answer in its simplest form.
Transcribed Image Text:(b) i. Use calculus to find the value of r which gives the minimum surface area of the solid. ii. Confirm that your value of r gives a minimum. (c) If the height of the solid with the minimum surface area is H cm, write down H the value of giving your answer in its simplest form.
(a) In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given byr³ and its curved surface area is given by 2². r cm Figure 3 h cm 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 the top of the cylinder. The volume of the solid is 5625π cm³. Express h in terms of r and hence show that the total surface area of the solid, A, is given by
Transcribed Image Text:(a) In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given byr³ and its curved surface area is given by 2². r cm Figure 3 h cm 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 the top of the cylinder. The volume of the solid is 5625π cm³. Express h in terms of r and hence show that the total surface area of the solid, A, is given by
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