what are the dimensions of two cylinders where the first cylinder has a greater surface area and the second cylinder has a greater volume?
2 answers
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let the height be h, and the radius be r
Volume = πr^2h
Surface area = 2πr^2 + 2πrh
volume > SA
πr^2h > 2πr^2 + 2πrh, divide by πr
rh > 2r + 2h
rh - 2h > 2r
h > 2r/(r-2)
if SA > volume
then h < 2r/(r-2)
for both to be true,
h = 2r/(r-2)
Volume = πr^2h
Surface area = 2πr^2 + 2πrh
volume > SA
πr^2h > 2πr^2 + 2πrh, divide by πr
rh > 2r + 2h
rh - 2h > 2r
h > 2r/(r-2)
if SA > volume
then h < 2r/(r-2)
for both to be true,
h = 2r/(r-2)
1 answer