The
diameter of a baseball is approximately 7.37 cm. A hockey puck is
cylindrical with a thickness

of
2.54 cm and a diameter of 7.6 cm. Which has the greatest volume?

**Solution:**

A
baseball is spherical and the volume of a sphere is (4/3)π

*r*^{3}. The radius of the sphere is half the diameter, so*r*= 3.685 cm. Using 3.14 for π, the volume of the baseball is (4/3)(3.14)(3.685)

^{3 }= 209.5 cm

^{3}.

^{ }(rounded to one decimal place)

The
volume of a cylinder is π

*r*^{2}*h*. The radius of the hockey puck is 3.8 cm, the height is 2.54 cm. Therefore the volume of the hockey puck is (3.14)(3.8)^{2}(2.54) = 115.2 cm^{3}. (rounded to one decimal place)
The
volume of a baseball is nearly double the volume of a hockey puck.

Suppose
you have a metal cone shaped container and a plastic container in the
shape of a shoe box. The cone shaped container is 14 inches high
with a diameter of 10 inches. The plastic container is 12 inches
long, 6 inches wide and 4 inches high. You want to fill up one
container with water. Which container will hold the most water?

**Solution:**

^{ }
The
volume of a cone is (1/3) π

*r*^{2}*h*.
Therefore,
the volume of the cone shaped container is (1/3)(3.14)(5)

^{2}(14) = 366.3 inches^{3 }(rounded to one decimal place)
The
volume of a rectangular solid is length times width times height,
therefore the volume of the plastic container is (12)(6)(4) = 288
inches

^{3}.
The
metal cone shaped container will hold the most water.

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