maths

Let the radius of the base be r, the height be h,

Volume = Area of the base X height
Area of the base = Area of a circle = r X r X π (π = 3.14159265)

Volume = r^2 π h

A solid right circular cylinder has length x metres and base radius r metres.The sum of the length and the circumference of its cross-section is 2 metres.
Find the maximum volume of the cylinder.

Circumference of cross-section
= 2πr m
Length
= x m

So we have
2πr + x = 2
r = (2-x)/2π .......... (*)

Volume of the cylinder
= (base area)(length)
= (πr²)(x)
= π[(2-x)/2π]²x
= π(4 - 4x + x²)x/4π²
= x(x² - 4x + 4)/4π
= (x³ - 4x² + 4x)/4π ....... (*)

直徑*3.14*高

Volume = π x r^2 x h

π : 3.14....
r : radius...
h : height

^^