Posted by admin | Posted in Uncategorized | Posted on 21-05-2009
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What percentage of the ball is under water?
A spherical ball filled with air has a radius 4 inches weighs 0.27 kg. It is placed in a pool. what percentage (in volume) of the ball is under the water?
Since the ball is floating, we see that:
F(buoyant) - F(weight of ball) = 0 ==> F(weight of ball) = F(buoyant).
Since F(buoyant) = pVg, we see that the volume of the ball under the water is:
F(weight of ball) = pVg
==> V = F(weight of ball)/(pg)
= m/p, since F(weight of ball) = mg, where m is the mass of the ball
= (0.27 kg)/(1000 kg/m^3)
≈ 2.7 x 10^-4 m^3.
Since 1 inch is about 2.54 cm = 0.0254 m, we see that:
1 in^3 = (0.0254 m)^3.
The volume of the ball in cubic inches is:
V = (4/3)πr^3, by the volume of a sphere
= (4/3)π(4 in)^3
= 256π/3 in^3.
In cubic meters, this is (256π/3)(0.0254)^3 ≈ 4.4 x 10^-3 m^3.
Therefore, the percentage of the ball under the water is:
(2.7 x 10^-4 m^3)/(4.4 x 10^-3 m^3) * 100 ≈ 6.1%.
I hope this helps!
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