Question

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

Answer 1

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.

Answer 2

(a)
$h = 4r$
$v \: {radii} = \pi \: r {}^{2} \times 4r$
$= 4\pi \times r {}^{3}$

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