
Convex surface area of cylinder,
$A = \pi dh$
Where:
$d = D \cos \theta$
$h = D \sin \theta$
$A = \pi (D \cos \theta)(D \sin \theta)$
$A = D^2 \pi \cos \theta \sin \theta$
$\dfrac{dA}{d\theta} = D^2\pi(\cos^2 \theta - \sin^2 \theta) = 0$
$\sin^2 \theta = \cos^2 \theta$
$\tan^2 \theta = 1$
$\theta = 45^\circ$
$d = D \cos 45^\circ = 0.707D$
$h = D \sin 45^\circ = 0.707D$
$\text{diameter} = \text{height}$ answer