SOLUTION: . Racquetball. The volume of rubber (in cubic centimeters) in a hollow rubber ball used in racquetball is given by where the inside radius is r centimeters and t

Question 181951: . Racquetball. The volume of rubber (in cubic centimeters)
in a hollow rubber ball used in racquetball is given by

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.
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.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
. Racquetball. The volume of rubber (in cubic centimeters)
in a hollow rubber ball used in racquetball is given by
.
Volume of a sphere = (4/3)(pi)r^3
"vol of rubber" ="Vol of outside radius sphere" - "Vol of inside radius sphere"
"vol of rubber" = (4/3)(pi)R^3 - (4/3)(pi)r^3
.
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.
"vol of rubber" = (4/3)(pi)R^3 - (4/3)(pi)r^3
"vol of rubber" = (4/3)(pi)(R^3 - r^3)
.
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.
.
Can't answer since I can't see the graph -- sorry.
But, I can answer it algebraically:
"vol of rubber" = (4/3)(pi)(R^3 - r^3)
Plug in what we know:
100 = (4/3)(3.14)(3^3 - r^3)
300 = 4(3.14)(27 - r^3)
75 = (3.14)(27 - r^3)
23.885 = 27 - r^3
3.115 = r^3
1.460 cm = r

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