+1712 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?
+1712 Wait: Don't I need to calculate the circle:
so that would be
2pir
12pi+72pi
84pi?
+36916 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)
+14917 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!
\(A_{hemisphere}=\frac{1}{2}\cdot A_{sphere}+A_{circle}\\ A_{hemisphere}=\frac{4\cdot \pi\cdot r^2}{2}+\pi\cdot r^2\\ A_{hemisphere}=3\cdot \pi \cdot r^2\)
\(A_{hsph\ r=6cm}=3\cdot \pi \cdot (6cm)^2=108cm^2\cdot \pi=339.292cm^2\)
!
