Question

a rectangular sheet of perimeter 27 cm and dimensions x cm by y cm is to be rolled into a cylinder. what values of x and y give the largest volume?

Answer 1

me first buhahaha

Answer 2

x = 2*pi*r
r = x/2pi

Answer 3

V = 1/(4pi) (27/2 * x^2 - x^3)
dV/dx = 1/(4pi) (27/2 * 2x - 3x^2)
dV/dx = 1/(4pi) (27x - 3x^2)

now, take dV/dx = 0
1/(4pi) (27x - 3x^2) = 0
multiply by 4pi to both sides, it can be
27x - 3x^2 = 0
then divide by -3, giving us
x^2 - 9x = 0
factor out!
x(x-9) = 0
the zeroes will satisfies only x = 9