Answer
(a.)$2048 \; mm^2$.
(b.)$2471\;mm^2 $.
Work Step by Step
Given values are:-
Radius $r=8.21\; mm$.
Height $h=39.7\; mm$.
(a.) Formula for the lateral surface area is
$A=2\pi rh$
Substitute all values.
$A=2\pi (8.21\;mm)(39.7\;mm)$
Simplify.
$A=2048 \; mm^2$ (rounded value.)
(b.) The area of the bases is
$=2\pi r^2$
Substitute all values.
$=2\pi (8.21)^2$
Simplify.
$=423 \; mm^2$ (rounded value.)
Total surface are
$=$ Lateral surface area $+$ Area of the bases.
Substitute all values.
$=2048\;mm^2+423\;mm^2 $
Simplify.
$=2471\;mm^2 $.
