How do you calculate the surface area of a cylinder using only the height and volume

Question

The volume is 2472,8cm² The height is is 23,4cm

Answer 1

Volume of a cylinder=πr²h where h is the height and r the radius.

Surface area=2πrh.

If the volume is V, then r²=V/(πh) and r=√(V/(πh)).

Therefore the surface area S=2πh√(V/(πh))=2√(Vπh). Since V and h are known and π=3.142 approx, S can be calculated.

EXAMPLE

If V=1000cm³ (1 litre) and h=10cm then 1000=10πr², so r=10/√π cm=5.642cm approx.

S=2πrh=112.84π=354.49cm² approx.

S=2√Vπh=2√10000π=200√π=354.49cm², using the formula S=2√(Vπh).