## Thursday, July 12, 2012

Consider these two problems involving volume.

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)πr3. 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 cm3. (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 cm3. (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) πr2h.

Therefore, the volume of the cone shaped container is (1/3)(3.14)(5)2(14) = 366.3 inches3 (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 inches3.

The metal cone shaped container will hold the most water.