Show that inner area of the tube is no less than outer area of 5 balls.
2007-12-27 07:27:40 · 5 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
tennisball (radius = r) has surface area A = 4πr^2
5 ball have surface area = 5A = 5*4πr^2 = 20πr^2
tube fitting 5 balls has radius = r and height h = 10r
tube's inner surface area (excluding bottom and top)
= 2πrh = 2πr(10r) = 20πr^2
= surface area of 5 balls
2007-12-27 07:38:00 · answer #1 · answered by sv 7 · 2⤊ 0⤋
If the balls have radius R, their total area is:
Aballs = 5*(4/3*Ï*R^3)
Aballs = 20/3*Ï*R^3
Assuming the balls have point contact with each other, and the tube is as small a cylinder as possible, the tube is 10*R tall and its inner area is:
Atube = Ï*R^2*h
Atube = Ï*R^2*(10*R)
Atube = 10*Ï*R^3
Now we compare the areas:
Atube > Aballs
10*Ï*R^3 > 20/3*Ï*R^3
10*Ï > 20/3*Ï
10 > 20/3
The inner area of the tube is larger than the outer area of the balls.
2007-12-27 15:35:45 · answer #2 · answered by lithiumdeuteride 7 · 1⤊ 1⤋
the amount of air around the tennis balls (but in the tube) can be refered as th inner area
so they r equal
2007-12-27 15:49:47 · answer #3 · answered by crystal 3 · 0⤊ 2⤋
What is the diameter of the balls?
2007-12-27 15:36:15 · answer #4 · answered by tercir2006 7 · 1⤊ 2⤋
i don't know, but i want to play tennis now.
woo
2007-12-27 15:43:54 · answer #5 · answered by collegebound17 2 · 0⤊ 1⤋