Question 118002
Your figure is a {{{cone}}}.

inside the long part  ({{{height}}} is {{{5ft }}}

and the bottom {{{diameter}}} is {{{8 ft}}} ……..that means a {{{radius=r}}} of base, which is a circle, is {{{r = 4ft}}}

so, the area {{{A}}} of this cone will be:


{{{A = r^2(Pi) + rL(Pi)}}}…where {{{L}}} is the {{{slant_height}}}
	

{{{A = (4ft)^2(Pi) + (4ft)L*(Pi)}}}…...now calculate {{{L}}} , to do it use Pythagorean Theorem


{{{L^2 = r^2 + h^2}}}

{{{L^2 = (4ft)^2 + (5ft)^2}}}

{{{L^2 = 16ft^2 + 25ft^2 }}}

{{{L^2 = 41ft ^2}}}


{{{L= sqrt(41ft^2) }}}

{{{L= 6.4ft}}}…we can round it to nearest whole number

{{{L =6ft }}}…….now, substitute it into {{{A}}}
	
{{{A = (4ft)^2(Pi) + (4ft)(6ft)(Pi)}}}…

{{{A = 16ft^2(Pi) + 24ft^2(Pi)}}}…

{{{A = 40ft^2(Pi) }}}……so, your answer is {{{a}}}