Question 1078575
The volume of a cone is volume = (1/3)(area of the base)(height),
so area of the base =3(volume)/height
The area of the base of this cone is
area of the base ={{{3*320pi/15=64pi}}} .
 
It would be good to know the radius, {{{r}}} , of that circular base.
The area of a circle of radius {{{r}}} is {{{pi*r^2}}} ,
so in this case {{{pi*r^2=64pi}}} --> {{{r^2=64}}} --> {{{r=8}}} .
 
At this point, you could look up a formula for the total area of a cone,
and apply it.
I looked up, and found
{{{area=pi*r*s+pi*r^2}}} , and
{{{area=pi*r*sqrt(h^2+r^2)+pi*r^2=pi*r*(sqrt(h^2+r^2)+r)}}}
with r, s, and h being
the radius of the base, the slant height, and the cone height.
 
{{{pi*r*sqrt(h^2+r^2)+pi*r^2=pi*8*sqrt(8^2+15^2)+pi*8^2=pi*8*sqrt(64+225)+pi*64=pi*8*sqrt(289)+64pi=pi*8*17+64pi=136pi+64pi=highlight(200pi)}}}
 
For those who want to understand rather than memorize formulas,
or use formulas without wondering why it is so:
The {{{pi*r^2}}} term represents the area of the circular base.
{{{s=qrt(h^2+r^2)}}} comes from the Pythagorean theorem 
applied to a cross section of the cone going through its axis.
The {{{pi*r*s}}} term represents the lateral area,
and that is an expression you could figure out by yourself, either
1) by considering the lateral area to be
the area of a pyramid with infinity of lateral faces
and a base perimeter of {{{2pi*r}}} , or
2) by thinking that the lateral area, peeled of and flattened out
would be a sector of a circle of area {{{pi*s^2}}} 
amounting to {{{2pi*r/2(pi*s)=r/s}}} of the entire circle).