Answer
(a.) $4520 \;cm^3$
(b.) $1380 \;cm^2$.
Work Step by Step
From the given figure we have
Diameter of the cone is $d=20.2\;cm$.
Radius $r=\frac{d}{2}$
$r=\frac{20.2}{2}\; cm$
$r=10.1\; cm$
Height of the cone is $h=42.3\;cm$.
(a.)
Formula of the volume of the cone is
$V=\frac{1}{3}\pi r^2 h$
Plug all values.
$V=\frac{1}{3}\pi (10.1\;cm)^2 (42.3\;cm)$
Simplify (rounded value).
$V=4520 \;cm^3$
(b.)
Formula for the slant height is
$s=\sqrt{r^2+h^2}$
plug all values.
$s=\sqrt{(10.1\;cm)^2+(42.3\;cm)^2}$
Simplify.
$s=43.49 \; cm$
Formula for the lateral surface area is
$A=\pi r s$
Plug all values.
$A=\pi (10.1\;cm) (43.49\;cm)$
Simplify (rounded value).
$A=1380 \;cm^2$.
