Answer:
total SA = 622.725mm^2
Step-by-step explanation:
we are trying to find the surface area of this structure
we can start by breaking this structure into three pieces.
(surface area of the left hemisphere)+(surface area of the right hemisphere)+(surface area of the right cylinder inbetween those 2 hemispheres)
1. surface area of the hemisphere.
surface area of a hemisphere is 4[tex]\pi[/tex][tex]r^2[/tex]
d = 8.4mm so r = 4.2mm.
surface area = [tex]4\pi (4.2)^2 = 221.670mm^2[/tex]
we need to take the half of 221.607 since it is half the hemisphere which is 221.670/2 = 110.835mm^2
we have two half hemisphere on the left and right so the tottal surface area of both the half hemisphere is 110.835x2 = 221.670mm^2
2. surface area of the right cylinder.
SA of right cylinder = [tex]2\pi rh[/tex]
[tex]2\pi (4.2)(15.2) = 401.118mm^2[/tex]
So the entire surface area is.
(surface area of both the half hemisphere + surface area of the right cylinder)
221.607+401.118 = 622.725mm^2
