A spherical ball is immersed in water contained in a vertical cylinder. The rise in water level is measured in order to calculate the raduis of the spherical ball. Calculate the radius of the ball in the following cases ..............................
a) cylinder of radius 10 cm, water level rises 4 cm
b) cylinder of radius 100 cm, water level rises 8 cm
please help i have no clue how to do it, i need help asap.. thx in advance
2007-03-01 21:54:05 · 3 answers · asked by Anonymous in Education & Reference ➔ Homework Help
I'll do the first one, you take the second.
The volume of a cylinder is pi r^2 h. In this case, the volume of water displaced by the sphere is a cylinder 10 cm in radius, 4 cm in height. That volume would be
V = pi (10 cm)^2 (4 cm) = 400 pi cm^3
The volume of a sphere is (4/3) pi r^3. Set this equal to the volume above:
(4/3) pi r^3 = 400 pi
The pi's drop out (thank Heaven)
(4/3) r^3 = 400
r^3 = 300
r = (300 cm^3)^(1/3) = 6.69 cm
The other works the same way.
2007-03-01 22:06:06 · answer #1 · answered by Anonymous · 0⤊ 0⤋
First we need to calculate the volume of the sphere which is the volume of the water displaced in the cylinder.
Where the cylinder has a radius of r = 10 cm:
Area of the cylinder = pi. r.r = pi.10.10 = 100 pi cm^2
Volume of 4 cm of water in such a cylinder = area X height
= 400 pi
Now this Volume V = 4.pi. r1^3/3 where r1 is the radius of the sphere.
r1^3 = 3.V/4.pi = 3.400 pi / 4 pi = 300
r = cubic root of 300 = 6.694 cm
For the second case where the radius of the cylinder is 100 cm, and the water level rises 8 cm, we can similarly work out that the radius of the sphere r2 is equal to
cubic root (3.R^2.H/4) where R is 100 cm and H = 8 cm.
The values are 6.694 cm and 39.1487 cm respectively.
2007-03-02 06:23:46 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
u got the answers u needed above.... i'll just note one thing: be careful with the units(cm etc) u use cause they may be tricky
2007-03-02 06:56:33 · answer #3 · answered by Anonymous · 0⤊ 0⤋