the diagram show a closed structure in the shape of a half cylinder. the diameter of each base is 16 feet. the length of the structure is 50 feet. Find the surface area of the entire structure.

Accepted Solution

Answer:The surface area is [tex]SA=(800+464\pi)\ ft^{2}[/tex]Step-by-step explanation:we know thatThe surface area of the half cylinder is equal to[tex]SA=2B+PL[/tex]whereB is the area of the half circleP is the perimeter of the half circle plus the diameter of circleL is the length of the structureFind the area BThe 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 diametersubstitute[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