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The marketing manager of a soft drink company wants to design a can with a height that is four times the radius of the can. a) express the volume of the can as a function of the radius, r b) explain the volume of the can as function of the height, h

Respuesta :

Volume of a cylindrical can  = pi r^2 h
We are given that  h = 4r ,  so substituting for h in the above formula:-
Volume = pi * r^2 * 4r  = 4pir^3 <----  the answer to Part a.

h = 4r  so r = h/4
Substituting for r:-
Volume = pi * (h/4)^2 * h = pi h^3/16 <------- Answer to part b.

mohk1112
(a)
[tex]h = 4r[/tex]
[tex]v \: {radii} = \pi \: r {}^{2} \times 4r \\ [/tex]
[tex] = 4\pi \times r {}^{3} [/tex]

(b)
[tex]4r = h [/tex]
[tex]r = \frac{h}{4} [/tex]
[tex]v \: {height} = \pi \times (\frac{h}{4} ) {}^{2} h[/tex]
[tex] = \pi( \frac{h {}^{3} }{16} )[/tex]