Word Problem: specific gravity of sphere of radius r

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vanbeersj

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The specific gravity of s of s phere of radius r that sinks to a depth h in water is given by s = (3rh^2-h^3)/4r^3. Find the depth to which a spherical buoy of radius 4.0 cm sinks if s = 0.50.

When I enter the values into the formula I'm left with

h^3-12h^2+96=0

This is where I'm having difficulties finding h.
 
Re: Word Problem

vanbeersj said:
The specific gravity of s of s phere of radius r that sinks to a depth h in water is given by s = (3rh^2-h^3)/4r^3. Find the depth to which a spherical buoy of radius 4.0 cm sinks if s = 0.50.

When I enter the values into the formula I'm left with

h^3-12h^2+96=0 <<< Show work - does not look correct

After getting the correct equation plot it in your graphing calculator. You'll find one root easily.

This is where I'm having difficulties finding h.
Click to expand...
 
Re: Word Problem

s= (3rh^2-h^3)/3r^3
0.5=(3(4)h^2-h^3)/3(4)^3
0.5=(12h^2-h^3)/192
96=12h^2-h^3
h^3-12h^2+96=0
 
Re: Word Problem

vanbeersj said:
s= (3rh^2-h^3)/4r^3
0.5=(3(4)h^2-h^3)/4(4)^3
0.5=(12h^2-h^3)/256
128=12h^2-h^3
h^3-12h^2+128=0

h=4 is one of the roots - find the others.
Click to expand...
 
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