## Thursday, October 4, 2012

Here's a little practice with word problems.

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.

The distance a tire rolls in one revolution is found by taking the circumference of the tire. If a tire has a diameter or 24 inches, how many revolutions must the tired make to cover a distance of 57 feet?

Solution:

The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle.

We need to get the units the same, so convert 24 inches to 2 feet.

C = π(2), using 3.14 as an approximation for π, C is approximately 6.28 feet.

To calculate the number of revolutions in 57 feet, take 57/(6.28) = 9.07. (rounded to 2 decimal places)