Wayne's class is building a wagon to be used as a float for the upcoming Pioneers Day Parade. The outsides of the four wagon wheels are going to be covered in brown felt so they can draw pictures on them. Rubber stripping will go around the wheel to help give it a smoother ride during the parade.

If each wheel has about 94.2 inches of rubber around it, the diameter of each wheel is inches.

Given this diameter, they need square inches of felt to cover each wheel.

If they can buy a rectangular piece of felt that has a width equal to the diameter of the wheel, the rectangular piece of felt would need to have a length of at least inches in order for each of the four wheel covers to be a solid piece. Though to account for any cutting errors, it should probably be a little longer.

Guest Jul 17, 2014

#1**+5 **

The circumference is 94.2 inches, and circumference is pi*diameter, so diameter = 94.2/pi inches.

Using 3.14 as an approximation for pi we get:

$${\mathtt{diameter}} = {\frac{{\mathtt{94.2}}}{{\mathtt{3.14}}}} \Rightarrow {\mathtt{diameter}} = {\mathtt{30}}$$

Diameter is 30 inches. So would need a length of at least 4*30 = 120 inches of felt for four wheels.

The area of the circular wheel is pi*diameter^{2}/4 square inches.

$${\mathtt{area}} = {\frac{{\mathtt{3.14}}{\mathtt{\,\times\,}}{{\mathtt{30}}}^{{\mathtt{2}}}}{{\mathtt{4}}}} \Rightarrow {\mathtt{area}} = {\mathtt{706.5}}$$

Area is 706.5 square inches. This much felt is needed to cover one wheel.

Alan
Jul 18, 2014

#1**+5 **

Best Answer

The circumference is 94.2 inches, and circumference is pi*diameter, so diameter = 94.2/pi inches.

Using 3.14 as an approximation for pi we get:

$${\mathtt{diameter}} = {\frac{{\mathtt{94.2}}}{{\mathtt{3.14}}}} \Rightarrow {\mathtt{diameter}} = {\mathtt{30}}$$

Diameter is 30 inches. So would need a length of at least 4*30 = 120 inches of felt for four wheels.

The area of the circular wheel is pi*diameter^{2}/4 square inches.

$${\mathtt{area}} = {\frac{{\mathtt{3.14}}{\mathtt{\,\times\,}}{{\mathtt{30}}}^{{\mathtt{2}}}}{{\mathtt{4}}}} \Rightarrow {\mathtt{area}} = {\mathtt{706.5}}$$

Area is 706.5 square inches. This much felt is needed to cover one wheel.

Alan
Jul 18, 2014