## Tuesday, September 4, 2012

Here's a few problems involving volume and comparing volumes:

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)πr^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 πr2h. 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) πr^2h.
Therefore, the volume of the cone shaped container is (1/3)(3.14)(5)^2(14) = 366.3 cubic inches (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 cubic inches.

The metal cone shaped container will hold the most water.