What is the surface area of this shape?

Needhelp4math

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A solid is constructed from a cylinder and two hemispheres with dimensions as shown. Find the Surface area
Answer is 1608
but im getting 2111.150263
Im honest done with math, i have a unit test tomorrow and at this rate im probably gonna skip it. All these questions add extra steps the teacher never goes over
a328349e6565605d1083df2348d22fcf.jpg
2b8e9b9021de67bfa2211aa874f570d3.jpg


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A solid is constructed from a cylinder and two hemispheres with dimensions as shown. Find the Surface area
Answer is 1608
but im getting 2111.150263
Im honest done with math, i have a unit test tomorrow and at this rate im probably gonna skip it. All these questions add extra steps the teacher never goes over
a328349e6565605d1083df2348d22fcf.jpg
2b8e9b9021de67bfa2211aa874f570d3.jpg


Sent from my LG-H831 using Tapatalk
.

SA = SA of cylinder + SA of 2 hemispheres = 2*pi*r*h + 2 * pi * r^2 + 2 * pi * r^2 = 2*3.14159*8* 16 + 4*3.14159*64 = 1608.495 = 1608

How (why?) did you get 3*pi*r^2? and the height of the cylinder is 16 - not 10.
 
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You have an open-ended cylinder and a sphere (2 semi-spheres).

cylinder: 2*pi*r*h
sphere: 4*pi*r^2

r = 8, h = 16

Were you too busy or tired to look up the formulas?
 
The picture of the shape is low quality so I didn't see the 16.
And i thought it LITERALLY meant 2 hemispheres that's why I used 3 pi r ^2.


One last question, why did you get rid of the 2 pi r ^2 on the cylinder formula?


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One last question, why did you get rid of the 2 pi r ^2 on the cylinder formula?

The formula for the TOTAL surface area of a cylinder is 2 pi r h + 2 pi r^2; that consists of two parts. The 2 pi r h is the lateral surface area (the sides), and that is all you need. The 2 pi r^2 is the area of the two circular ends, which are not part of your surface, so you can't include them.

I consider it far better to memorize, not the total surface area formula, but the two formulas separately:

Lateral surface area = 2 pi r h
End surface area (each) = pi r^2

Then you can put together whatever pieces you need for a particular problem, rather than cut off and throw away the ends of a can when you don't need them!
 
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