Question 181953
Racquetball. The volume of rubber (in cubic centimeters)
in a hollow rubber ball used in racquetball is given by 
V=4/3 R3^3-4/3 r^3 
{{{V=4*pi*R3^3/3-4*pi*r^3/3}}} pi was left out
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where the inside radius is r centimeters and the outside
radius is R centimeters.
a) Rewrite the formula by factoring the right-hand side
completely.
{{{4*pi*R3^3/3-4*pi*r^3/3}}}
={{{(4*pi/3)*(R^3 - r^3)}}} Factoring this far would be useful.
={{{(4*pi/3)*(R-r)*(R^2 + R*r - r^2)}}} There's no advantage to this.
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b) The accompanying graph shows the relationship
between r and V when R =3. Use the graph to
estimate the value of r for which V = 100 cm3.
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I don't see a graph.
It says V is the volume of rubber.  100 cc seems like a lot.
The OD of a ball is 5.7 mm, so R = 2.85 cm
The total volume of the rubber and the gas inside the ball is:
{{{4*pi*2.85^3/3}}}
V =~96.967 cc
Obviously, the composer of the problem now refers to V as the total volume, a lack on consistency.
To make a graph of this (or anything else) go to www.padowan.dk.com/graph/ and DL the (free) software.