✔ 最佳答案
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.
