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The standard aluminium drink can is designed to hold 375ml. The main variables for the can are height h, centimetres and radius r, centimetres. 7. (a) If volume, V= 375, write an expression for h in terms of r. (b) Use (a) to write an expression for surface area, S in terms of r. (c) Differentiate the expression for S with respect to r. (d) The manufacturer would like to use the smallest amount of aluminium. If he does, what would be the radius of the drink can? (e) With the radius in (d), what will the height of the can have to be? (f) Are standard aluminium drink cans this size? Comment on what you find when you compare the dimensions of a can which uses the minimum amount of aluminium with an actual can. (7) V=375 ml ; h=cm r = Cm a) 375=TTr?h h= 375 b) s 2 2Trh + 2TTY 2 = 2 TTr (375) + 2T r S= 750 C) Scr) = -7so xL +2T C2x) Simplits 2 s'cr> ==750 t 4TT r 3

The standard aluminium drink can is designed to hold 375ml. The main variables for the can are height h, centimetres and radius r, centimetres. 7. (a) If volume, V= 375, write an expression for h in terms of r. (b) Use (a) to write an expression for surface area, S in terms of r. (c) Differentiate the expression for S with respect to r. (d) The manufacturer would like to use the smallest amount of aluminium. If he does, what would be the radius of the drink can? (e) With the radius in (d), what will the height of the can have to be? (f) Are standard aluminium drink cans this size? Comment on what you find when you compare the dimensions of a can which uses the minimum amount of aluminium with an actual can. (7) V=375 ml ; h=cm r = Cm a) 375=TTr?h h= 375 b) s 2 2Trh + 2TTY 2 = 2 TTr (375) + 2T r S= 750 C) Scr) = -7so xL +2T C2x) Simplits 2 s'cr> ==750 t 4TT r 3

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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O 56% 5:00 AM Tue 12 Oct Assignment 4 Ananya S- 2021-94 F+Assignment+4 Assignment 4 Ananya S T The standard aluminium drink can is designed to hold 375ml. The main variables for the can are height h, centimetres and radius r, centimetres. 7. (a) If volume, V = 375, write an expression for h in terms of r. (b) Use (a) to write an expression for surface area, S in terms of r. (c) Differentiate the expression for S with respect to r. (d) The manufacturer would like to use the smallest amount of aluminium. If he does, what would be the radius of the drink can? (e) With the radius in (d), what will the height of the can have to be? (f) Are standard aluminium drink cans this size? Comment on what you find when you compare the dimensions of a can which uses the minimum amount of aluminium with an actual can. (7) V=375 ml h=cm = cm r a) 375=TTp?h h= 375 b) s 2 2Trh+ 2TTY 2 = 2 TTrr375 S= 750 c) Scr) = -7so xL +2T C2x) Simplits z s'cr) 3 =-750 t 4TT r
Transcribed Image Text:O 56% 5:00 AM Tue 12 Oct Assignment 4 Ananya S- 2021-94 F+Assignment+4 Assignment 4 Ananya S T The standard aluminium drink can is designed to hold 375ml. The main variables for the can are height h, centimetres and radius r, centimetres. 7. (a) If volume, V = 375, write an expression for h in terms of r. (b) Use (a) to write an expression for surface area, S in terms of r. (c) Differentiate the expression for S with respect to r. (d) The manufacturer would like to use the smallest amount of aluminium. If he does, what would be the radius of the drink can? (e) With the radius in (d), what will the height of the can have to be? (f) Are standard aluminium drink cans this size? Comment on what you find when you compare the dimensions of a can which uses the minimum amount of aluminium with an actual can. (7) V=375 ml h=cm = cm r a) 375=TTp?h h= 375 b) s 2 2Trh+ 2TTY 2 = 2 TTrr375 S= 750 c) Scr) = -7so xL +2T C2x) Simplits z s'cr) 3 =-750 t 4TT r
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