Mathematics: 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.

The diagram show a closed structure in the shape

cheergirlkr4746

09.03.2022

The surface area is $SA=(800+464\pi)\ ft^{2}$

Step-by-step explanation:

we know that

The surface area of the half cylinder is equal to

SA=2B+PL

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

$B=\frac{1}{2} \pi r^{2}$

we have

$r=16/2=8\ ft$ -----> the radius is half the diameter

substitute

$B=\frac{1}{2} \pi (8)^{2}$

$B=32\pi\ ft^{2}$

Find the value of P (the perimeter of the half circle plus the diameter of circle)

$P=\pi r+D$

we have

$D=16\ ft$

$r=8\ ft$

substitute

$P=\pi (8)+16$

$P=(8\pi+16)\ ft$

Find the surface area

SA=2B+PL

$L=50\ ft$

substitute

$SA=2(32\pi)+(8\pi+16)(50)$

$SA=64\pi+400\pi+800$

$SA=(800+464\pi)\ ft^{2}$

see the attached figure to better understand the problem

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