Question

At a local park, Justin can choose between two circular paths to ride his bicycle. One path has a diameter of 105 yards, and the other has a radius of 40 yards. How much farther can Justin ride his bike on the longer path than the shorter path if he rides his bike around the path once? Use 3.14 for pi.

a) 210 yards
b) 420 yards
c) 630 yards
d) 840 yards

Answer 1

Justin can ride his bike approximately 78.8 yards farther on the longer path compared to the shorter path.

Step-by-step explanation:

To find the circumference of a circle, we use the formula C = 2πr, where C is the circumference and r is the radius. We are given the diameter of the longer path, which is 105 yards. To find the circumference of this path, we need to divide the diameter by 2 to get the radius. Therefore, the radius of the longer path is 105/2 = 52.5 yards. Substituting this value into the formula, we get C = 2 x 3.14 x 52.5 = 330 yards.

Similarly, to find the circumference of the shorter path, we can use the formula C = 2πr. The radius of the shorter path is given as 40 yards, so substituting this value into the formula, we get C = 2 x 3.14 x 40 = 251.2 yards.

The difference in distance between the longer and shorter paths can be found by subtracting the circumference of the shorter path from the circumference of the longer path: 330 - 251.2 = 78.8 yards.

Therefore, Justin can ride his bike approximately 78.8 yards farther on the longer path compared to the shorter path.