Question 1020868
The total surface area, SA, is the sum of the lateral surface area and twice the area of the base, i.e., 

SA  = LA + 2B ==> SA = 10(circumference)+ 2B

= {{{10*2*pi*r+ 2*pi*r^2 = 20*pi*r+2*pi*r^2}}}

==> {{{20*pi*r+2*pi*r^2 = 112*pi}}}

==> {{{r^2 + 10r = 56}}} after making the necessary cancellations,

==> {{{r^2 + 10r - 56=0}}} ==> (r+14)(r-4) = 0

==> r = 4.  (r cannot be equal to -14 for obvious reasons.)
==> The diameter of the right circular cylinder is 8.