<PRE><B>Question 849775</B>
The volume and curved surface area of a cylinder are 1650cm^3 and 660cm^2 respectively.
 Find the radius and height of the cylinder.
:
let r = the radius
let h = the height
:
Volume: {{{pi*r^2*h}}} = 1650
Curved surface: {{{2pi*r*h}}} = 660
make both equations = to h
h = {{{1650/(pi*r^2)}}}
and
h = {{{660/(2pi*r)}}} = {{{330/(pi*r)}}}
therefore
{{{330/(pi*r)}}} = {{{1650/(pi*r^2)}}}
multiply both sides by {{{pi*r}}} and you have
330 = {{{1650/r}}}
r = {{{1650/330}}}
r = 5 cm is the radius
:
Find the height
h - {{{330/(pi*5)}}}
h - {{{330/15.7)}}}
h = 21.0 cm is the height
:
:
Check this by finding the volume with these values
V = {{{pi*5^2*21}}}
V = 1649.33, a slight error from rounding off

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