[急]A math question about cylinder－elahism的部落格

標題:

[急]A math question about cylinder

發問:

if you have the area and volume of a cylinder, how can you find the radius and height of the cylinder. pls answer that question. 急更新: can somebody make "r" on one side like "r = ......." my math skill is not very good i need help it is for programming :)

最佳解答:

Let The the base radius be r, and the height be h. Surface Area of the cylinder = area of two base + area of the curved surface = 2 x (pi)(r^2) + 2(pi)(r)(h) = 2(pi)(r)(r+h) Volume of the cylinder = base area x height = (pi)(r^2)(h) so, now we have the area and volume fo the cylinder Let them be A and V respectively. 2(pi)(r)(r+h) = A...(1) (pi)(r^2)(h) = V...(2) from (2) h = V / [(r^2)(pi)]...(3) Sub (3) into (1) 2(pi)(r){r+V/[(r^2)(pi)]} = A (r){r+V/[(r^2)(pi)]} = A/[2(pi)] r^2 + V/[(pi)(r)] = A/[2(pi)] (pi)r^3 + V = Ar/2 V = Ar/2 - (pi)(r^3) V = r[(A/2) - (pi)(r^2)] As V and A is known, with 1 equation and 1 unknown (r), we can know r. put the value of r back to (1) or (2), we can know h.

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