SOLUTION: A cylindrical can holds three tennis balls. each ball has a diameter of 6 cm, which is the same diameter as the cylinder, and the cylinder is filled to the top. Calculate the volum

Algebra ->  Volume -> SOLUTION: A cylindrical can holds three tennis balls. each ball has a diameter of 6 cm, which is the same diameter as the cylinder, and the cylinder is filled to the top. Calculate the volum      Log On


   

Question 1207242: A cylindrical can holds three tennis balls. each ball has a diameter of 6 cm, which is the same diameter as the cylinder, and the cylinder is filled to the top. Calculate the volume of space in the cylinder not taken up by the tennis balls. Round to the nearest cubic centimeter
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A cylindrical can holds three tennis balls. each ball has a diameter of 6 cm,
which is the same diameter as the cylinder, and the cylinder is filled to the
top. Calculate the volume of space in the cylinder not taken up by the tennis
balls. Round to the nearest cubic centimeter
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The formula in the post by @josgarithmetic for the empty volume

        18%2Api%2A%286%2F2%29%5E2-%284%2F3%29pi%2A%286%2F2%29%5E2  cubic centimeters

is  FATALLY  INCORRECT.  A correct formula is

        18%2Api%2A%286%2F2%29%5E2-3%2A%284%2F3%29pi%2A%286%2F2%29%5E3  cubic centimeters.

It gives the value of   3.14159265%2A%2818%2A%286%2F2%29%5E2-3%2A%284%2F3%29%2A%286%2F2%29%5E3%29 = 339.292  cm^3.

Notice that for the given configuration, the empty space is exactly half of the occupied space.

It was known just to  Archimedes about  2300  years ago,  when he discovered the formula for the volume of a sphere.