SOLUTION: The totel surface area of a cylinder og height H, and base radius R, is treble that of another cylinder of the same radius R ut of height h. Prove that {{{R=(H-3h)/2}}}

Algebra ->  Algebra  -> Volume -> SOLUTION: The totel surface area of a cylinder og height H, and base radius R, is treble that of another cylinder of the same radius R ut of height h. Prove that {{{R=(H-3h)/2}}}      Log On

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Question 177916: The totel surface area of a cylinder og height H, and base radius R, is treble that of another cylinder of the same radius R ut of height h. Prove that
R=%28H-3h%29%2F2
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
V=2%28pi%29r%5E2+%2B+2%28pi%29r%2Ah--->remember r=R
:
3V=2%28pi%29R%5E2+%2B+2%28pi%29R%2AH
:
in order for these 2 equations to be equal we have to multiply the smaller Volume by 3
:
:
3%282%28pi%29R%5E2+%2B+2%28pi%29R%2Ah%29=%282%28pi%29R%5E2+%2B+2%28pi%29R%2AH%29
:
6%28pi%29R%28R%2Bh%29=2%28pi%29R%28R%2BH%29factoring 6%28pi%29R on left and 2%28pi%29Ron the right
:
3%28R%2Bh%29=R%2BHdivided both sides by 2%28pi%29R
:
3R%2B3h=R%2BHdistributed left side
:
2R=H-3hsubtracted R and 3h from both sides
:
highlight%28R=%28H-3h%29%2F2%29....divided both sides by 2