Answer
(a.)$6367\;cm^2$
(b.)$8781\;cm^2$.
Work Step by Step
Given values are:-
Diameter $d=39.2\; cm$
Radius $r=\frac{d}{2}$ $r=\frac{39.2}{2}\;cm$ $r=19.6\;cm$
Height $h=51.7\; cm$.
(a.)
Formula for the lateral surface area is $A=2\pi rh$.
Substitute all values.
$A=2\pi (19.6\;cm)(51.7\;cm)$
Simplify.
$A=6367 \; cm^2$ (Rounded value.)
(b.) The area of the bases
$=2\pi r^2$
Substitute all values.
$=2\pi (19.6\;cm)^2$
Simplify.
$=2414 \; cm^2$ (rounded value.)
Total surface are
$=$ Lateral surface area $+$ Area of the bases.
Substitute all values.
$=6367\;cm^2+2414\;cm^2 $
Simplify.
$=8781\;cm^2 $.
