Question 157683
I'm assuming the building is a cylinder with a hemisphere roof.
The cylinder surface are is the perimeter of the circle (hemisphere) multiplied by the height of the cylinder.
The height of the cylinder is the total height minus the hemisphere radius.
{{{SA[c]=2*pi*R*(H[t]-R)}}}
{{{SA[c]=2*pi*10*(24-10)}}}
{{{SA[c]=2*pi*10*(14)}}}
{{{SA[c]=280*pi}}}
The surface area of the hemisphere is 1/2 the surface area of a sphere with radius 10 ft.
{{{SA[s]=(1/2)*4*pi*R^2}}}
{{{SA[s]=2*pi*10^2}}}
{{{SA[s]=200*pi}}}
THe total surface is the sum of these two.
{{{SA[t]=SA[c]+SA[s]}}}
{{{SA[t]=280*pi+200*pi}}}
{{{SA[t]=480*pi}}}
or approximately
{{{SA[t]=1508}}}
1508 sq. ft.