Volume:

$V = \dfrac{1}{4}\pi d^2 h = \, \text{ 1 quart }$

$\dfrac{1}{4}\pi \left[ d^2 \dfrac{dh}{dd} + 2dh \right] = 0$

$\dfrac{dh}{dd} = -\dfrac{2h}{d}$

Total area (closed both ends):

$A_T = 2(\frac{1}{4}\pi d^2)+ \pi d \, h$

$A_T = \frac{1}{2}\pi d^2 + \pi d \, h$

$\dfrac{dA_T}{dd} = \pi d + \pi \left[ d\dfrac{dh}{dd} + h \right] = 0$

$d d\dfrac{dh}{dd} + h = 0$

$d + d\left( -\dfrac{2h}{d} \right) + h = 0$

$d = h$

Diameter = height *answer*