Answer:
The surface area is [tex]SA=(800+464\pi)\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the half cylinder is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the half circle
P is the perimeter of the half circle plus the diameter of circle
L is the length of the structure
Find the area B
The area of the half circle is
[tex]B=\frac{1}{2} \pi r^{2}[/tex]
we have
[tex]r=16/2=8\ ft[/tex] -----> the radius is half the diameter
substitute
[tex]B=\frac{1}{2} \pi (8)^{2}[/tex]
[tex]B=32\pi\ ft^{2}[/tex]
Find the value of P (the perimeter of the half circle plus the diameter of circle)
[tex]P=\pi r+D[/tex]
we have
[tex]D=16\ ft[/tex]
[tex]r=8\ ft[/tex]
substitute
[tex]P=\pi (8)+16[/tex]
[tex]P=(8\pi+16)\ ft[/tex]
Find the surface area
[tex]SA=2B+PL[/tex]
[tex]L=50\ ft[/tex]
substitute
[tex]SA=2(32\pi)+(8\pi+16)(50)[/tex]
[tex]SA=64\pi+400\pi+800[/tex]
[tex]SA=(800+464\pi)\ ft^{2}[/tex]
see the attached figure to better understand the problem
