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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.

 

 

Work/confusion:

I know that a hemisphere is half a sphere, so I cut the equation in half, which got me to:

\(\frac{4*pi*r^2}{2} \\=2*pi*r^2\)

After that, I have NO idea what to do...

Edit: I do, but I want to make sure I'm right so far

 

A hint, please?

 Dec 7, 2019
edited by tommarvoloriddle  Dec 7, 2019
edited by tommarvoloriddle  Dec 8, 2019
 #1
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Just put in the value given to you for r

 Dec 8, 2019
 #2
avatar+1694 
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Am I correct about halving the equation?

tommarvoloriddle  Dec 8, 2019
 #3
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Absolutely !

ElectricPavlov  Dec 8, 2019
 #4
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yay so I get this:

tommarvoloriddle  Dec 8, 2019
 #5
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2* pi *6^2

 

2*pi*36

 

72pi

 

Am I right?

 Dec 8, 2019
 #7
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Yeppers....you got it !

ElectricPavlov  Dec 8, 2019
 #9
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Wooot!

Thx!

tommarvoloriddle  Dec 8, 2019
 #6
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*****************

 Dec 8, 2019
edited by ElectricPavlov  Dec 8, 2019
 #8
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So I am right~

Thank you!

tommarvoloriddle  Dec 8, 2019
 #10
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Wait: Don't I need to calculate the circle:

 

so that would be

 

2pir

 

12pi+72pi

 

84pi?

 Dec 8, 2019
 #11
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Don't overthink it...... if total surface area is 4 pi r^2    you want 1/2 of this    2 pi r^2    = 72 pi

 

The way the question is worded is a bit unclear.....I think you may be right, you will need to add the area of the base (the' cut' area of the sphere)

  (pi r^2)                                 (2 pi r is the circumference)

ElectricPavlov  Dec 8, 2019
edited by ElectricPavlov  Dec 8, 2019
 #14
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WHoops!

tommarvoloriddle  Dec 8, 2019
 #12
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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.

 

Die Oberfläche einer Kugel mit dem Radius r beträgt 4 pir ^ 2. Wie groß ist die Gesamtfläche einer Halbkugel mit einem Radius von 6 cm einschließlich der Fläche ihrer kreisförmigen Basis? Drücken Sie Ihre Antwort in Form von pi aus.

 

Hello tommarvoloriddie!

 

\(A_{hemisphere}=\frac{1}{2}\cdot A_{sphere}+A_{circle}\\ A_{hemisphere}=\frac{4\cdot \pi\cdot r^2}{2}+\pi\cdot r^2\\ A_{hemisphere}=3\cdot \pi \cdot r^2\)

 

\(A_{hsph\ r=6cm}=3\cdot \pi \cdot (6cm)^2=108cm^2\cdot \pi=339.292cm^2\)

laugh  !

 Dec 8, 2019
edited by asinus  Dec 8, 2019
edited by asinus  Dec 8, 2019
 #13
avatar+1694 
+1

Thank you!!!!!!!

tommarvoloriddle  Dec 8, 2019

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