Answer
(a.) $1010\;cm^3$.
(b.) $427\; cm^2$.
Work Step by Step
From the given figure we have
Diameter of the cone is $d=16.0\;cm$.
Radius $r=\frac{d}{2}$
$r=\frac{16.0}{2}\; cm$
$r=8.0\; cm$
Height of the cone is $h=15.0\;cm$.
(a.)
Formula of the volume of the cone is
$V=\frac{1}{3}\pi r^2 h$
Plug all values.
$V=\frac{1}{3}\pi (8.0\;cm)^2 (15.0\;cm)$
Simplify (rounded value).
$V=1010 \;cm^3$
(b.)
Formula for the slant height is
$s=\sqrt{r^2+h^2}$
plug all values.
$s=\sqrt{(8.0\;cm)^2+(15.0\;cm)^2}$
Simplify.
$s=17.0 \; cm$
Formula for the lateral surface area is
$A=\pi r s$
Plug all values.
$A=\pi (8.0\;cm) (17.0\;cm)$
Simplify (rounded value).
$A=427 \;cm^2$.
