Please see attachment.
Hi
Let R be the radius of the cylinder and L its length
The volume is $\displaystyle V_0 = \pi R^2L + \frac43 \pi R^3 = 13.4 cm^3$
From this expression you can find L as a function of R
The area is $\displaystyle A(R,L) = 2\pi RL + 4 \pi R^2$
Substitute L function of R to get A(R)
Calculate A'(R) to find the value of R which minimizes the area