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A cylinder with height 2x is inscribed in a sphere with radius 10. a. Show that the volume of the cylinder, V, is 2Tx(100 - x). b. By using_calculus, one can show that V is maximum when 10V3 Substitute this value for x to find the maximum 3 volume V. c. (Optional) Use a calculator or a computer to evaluate V = 2nx(100 - x) for various values of x between 0 and 10. Show that the maximum volume V occurs when x = 5.77. 10 Exs. 30, 31

A cylinder with height 2x is inscribed in a sphere with radius 10. a. Show that the volume of the cylinder, V, is 2Tx(100 - x). b. By using_calculus, one can show that V is maximum when 10V3 Substitute this value for x to find the maximum 3 volume V. c. (Optional) Use a calculator or a computer to evaluate V = 2nx(100 - x) for various values of x between 0 and 10. Show that the maximum volume V occurs when x = 5.77. 10 Exs. 30, 31

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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A cylinder with height 2x is inscribed in a sphere with radius 10. a. Show that the volume of the cylinder, V, is 2Tx(100 - x). b. By using_calculus, one can show that V is maximum when 10V3 Substitute this value for x to find the maximum 3 volume V. c. (Optional) Use a calculator or a computer to evaluate V = 2nx(100 - x) for various values of x between 0 and 10. Show that the maximum volume V occurs when x = 5.77.
Transcribed Image Text:A cylinder with height 2x is inscribed in a sphere with radius 10. a. Show that the volume of the cylinder, V, is 2Tx(100 - x). b. By using_calculus, one can show that V is maximum when 10V3 Substitute this value for x to find the maximum 3 volume V. c. (Optional) Use a calculator or a computer to evaluate V = 2nx(100 - x) for various values of x between 0 and 10. Show that the maximum volume V occurs when x = 5.77.
10 Exs. 30, 31
Transcribed Image Text:10 Exs. 30, 31
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