Answer: Option D.
[tex]A =96\pi\ cm^2[/tex]
Step-by-step explanation:
The area of the circular bases is:
[tex]A_c = 2\pi(a) ^ 2[/tex]
Where
[tex]a=4\ cm[/tex] is the radius of the circle
Then
[tex]A = 2\pi(4) ^ 2[/tex]
[tex]A = 32\pi\ cm^2[/tex]
The area of the rectangle is:
[tex]A_r=b * 2\pi r[/tex]
Where
[tex]b=8\ cm[/tex]
b is the width of the rectangle and [tex]2\pi r[/tex] is the length
Then the area of the rectangle is:
[tex]A_r=8 * 2\pi (4)[/tex]
[tex]A_r=64\pi\ cm^2[/tex]
Finally the total area is:
[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]
[tex]A =96\pi\ cm^2[/tex]
