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4 answers

Your equation for sphere volume is wrong.

V = (4/3)*π*r^3 = 32*π/3
dV = (4/3)*π*3*r^2*dr = (4/3)*π*3*(2)^2*(1.9-2) = -8*π/5

The change in volume as a percent is:

dV/V = -(8*π/5)/(32*π/3) = -3/20 = -15%
So the volume decreased by 15%, as you suspected.

2007-12-11 00:55:57 · answer #1 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 1 0

Your equation should be: V=(4/3)*pi*(r)^3

The best way to calculate percentage change is to take logarithms on both sides (doesn't matter which base in the long term). Just take log base e (i.e. ln).

ln(V)= ln(4/3*pi) + 3 ln (r)

Now take differentials on both sides (or differentiate w.r.t. r; doesn't matter).

dV/V = 3* dr/r

So this can be approximated: (V1 - V2)/V1 = 3* (r1 - r2)/r1

r1= 2.0, r2= 1.9. The left hand side of the equation obviously gives % change in V when multiplied by 100.

2007-12-11 01:09:00 · answer #2 · answered by Deep B 2 · 0 1

Should be r³ in equation.
V1 = (4/3) π ( 2 ³ ) = (4/3) π (8)
V2 = (4/3) π (1.9 ³ )

V2/V1 = 1.9 ³ / 8 = 0.86 = 86%
Change in volume = 14%

2007-12-11 03:51:15 · answer #3 · answered by Como 7 · 2 0

yep,
your equation is wrong, Volume of sphere is
V=4/3(pi)r^3.

2007-12-11 01:09:11 · answer #4 · answered by Pramod D 1 · 0 1

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