Surface Area of a Cylinder isn't that. It's the area of the two circular sections (2πr^2) Added to the longitudinal area (I don't know what this is called) which is 2πrh
2πr^2+2πrh = πr^2h
And solve for h.
The problem is as follows:
The total surface area of a cylinder is numerically the same as its volume.
The radius of the cylinder is rcm, the height is hcm.
Express h in terms of r.
The answer is h = 2r / (r – 2)
Surface area of cylinder = hπ2r (π is the symbol for pi)
Volume of cylinder = hπr^2
If the volume and area are numerically the same then I assume
hπ2r = hπr^2
By dividing both sides by π
h2r = hr^2
At this point I am stuck (assuming the previous steps are correct). Can anyone help?
Thanks in advance
Lewis
Thanks Quacky and Topquarks,
Yes I did forget the end caps. I assumed it was a hollow cylinder.
Here is the solution if anyone is interested
2πr^2 + 2πrh = hπr^2
Divide by π
2r^2 + 2rh = hr^2
Bring all the h terms onto one side
2r^2 = hr^2 - 2rh
Isolate the h term
2r^2 = h(r^2 - 2r)
2r^2 / (r^2 - 2r) = h
Simplify the form of the denominator
2r^2 / r(r - 2) = h
Cancel (divide) the r’s in the numerator and denominator
2r / (r - 2) = h
And we have the answer.