Question 1036916
Find the dimensions of a cylindrical container with a volume of 40 cubic inches and a side area of 60 square inches
:
let r = the radius of the container
let h = the height
:
Volume: {{{pi*r^2*h}}} = 40 cu/in
h = {{{40/(pi*r^2)}}}
:
Side area: {{{2*pi*r*h}}} = 60 cu/in
divide both sides by 2
{{{pi*r*h}}} = 30
h = {{{30/(pi*r)}}} 
:
h=h, therefore
{{{40/(pi*r^2)}}} = {{{30/(pi*r)}}}
multiply both sides by pi*r
{{{40/r}}} = 30
30r = 40
r = 40/30
r = 1{{{1/3}}} inches is radius
Find h
h = {{{30/(pi*1.333)}}}
h = 7.164 inches is the height
:
:
Confirm these values in the Vol formula
V = {{{pi*1.333^2*7.164}}}
V = 40