Practice and Connect

For example, if you use 3cm as the radius of your wheels,

The distance the toy goes will be the same as the circumference of a circle. In the case of one full rotation, using the equation C=2•𝜋•r, you get 2 x 3.14 x 3 cm, so the distance is approximately 18.84 cm.

For example, if you use 3cm as the radius of your wheels,

If the wheels make three full rotations, the distance the toy goes is 3 times further than the distance it goes for one full rotation. This is 3 times the circumference of the wheels, so 3 x 18.84 cm from the previous answer, which is approximately 56.52 cm.

For example, if you use 3cm as the radius of your wheels,

Since the radius of the wheels of the new toy is twice as long, it is 2 x 3 cm, so 6 cm in radius. The distance the new toy goes in one full rotation would be using the circumference equation again, C=2•𝜋•r, you get 2 x 3.14 x 6 cm, so the distance is approximately 37.68 cm. Some students may notice that if the radius is twice as long, the circumference also becomes twice as long. Therefore the distance the new toy covers in one full rotation will be twice as long as the distance covered by the original toy.

From the previous problems, students learned that when a toy goes for one full rotation, it is the same as the circumference of the wheel. So, if the toy goes 15 cm for one full rotation, the circumference of the wheels is also 15 cm. So what is the radius, r, in the equation 15 = 2 x 3.14 x r? It is approximately 2.39 cm.