SOLUTION: . 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 where the inside radius

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: . 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 where the inside radius       Log On


   



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


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 Alan3354(69443) About Me  (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
V=4/3 R3^3-4/3 r^3
V=4%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3 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%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3
=%284%2Api%2F3%29%2A%28R%5E3+-+r%5E3%29 Factoring this far would be useful.
=%284%2Api%2F3%29%2A%28R-r%29%2A%28R%5E2+%2B+R%2Ar+-+r%5E2%29 There's no advantage to this.
-----------------------
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.
-------------------
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%2Api%2A2.85%5E3%2F3
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.