Question 1199778
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A = surface area of the cylinder
B = surface area of the hemisphere
We'll use this to find A+B, but we'll do a bit of adjustment as I'll explain later.


r = radius = diameter/2 = 9/2 = 4.5 cm
h = height = 9 cm



Cylinder:
surface area of cylinder = 2pi*r^2 + 2pi*r*h
surface area of cylinder = 2pi*r(r + h)
A = 2pi*r(r + h)
A = 2pi*4.5(4.5 + 9)
A = 121.5pi


Hemisphere:
surface area of hemisphere = (area of circular base)+(half of surface area of sphere)
B = (pi*r^2) + (0.5*(4pi*r^2))
B = pi*r^2 + 2pi*r^2
B = 3pi*r^2
B = 3pi*(4.5)^2
B = 60.75pi


A+B = 121.5pi + 60.75pi
A+B = 182.25pi


It appears choice (b) is the final answer. 
But be careful: this is trick/trap your teacher set up.


The calculation A+B counts the circular base of the hemisphere and the circular top of the cylinder.
These two circles are NOT part of the external surface area. 
They are covered up when the shapes combine.
Think of them as internal walls that are not part of the exterior of the house.


We'll subtract off two copies of pi*r^2 = pi*(4.5)^2 = 20.25pi
So we subtract 2*20.25pi = 40.5pi square cm of area.


182.25pi - 40.5pi = 141.75pi


Answer: <font color=red size=4>a)  141.75pi</font>
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