SOLUTION: A wooden right circular cylinder with diameter 9 cm and height 9 cm is topped with a hemisphere. The surface area, in cm^2, of the resulting shape is
a) 141.75π
b) 182.25π
c
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-> SOLUTION: A wooden right circular cylinder with diameter 9 cm and height 9 cm is topped with a hemisphere. The surface area, in cm^2, of the resulting shape is
a) 141.75π
b) 182.25π
c
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Question 1199778: A wooden right circular cylinder with diameter 9 cm and height 9 cm is topped with a hemisphere. The surface area, in cm^2, of the resulting shape is
a) 141.75π
b) 182.25π
c) 162π
d) 405π
e) 182.25 + 60.75π Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
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.
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