Question

a wheel of a childs bicycle has a circumference that is 50% of the circumference of a childs mountain bicycle wheel. the childs bicycle wheel has a circumference of 37.7 inches. what is the radius (to the nearest inch) of the childs bicycle wheel? of the childs mountain bicycle wheel?
6 in; 3 in
12 in; 6 in
6 in; 12 in
6 in; 8 in.

Explanation:

Step1: Recall circumference formula

The formula for the circumference of a circle is $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius.

Step2: Find radius of child's bicycle wheel

We know $C = 37.7$ inches for the child's bicycle wheel. Rearranging the formula for $r$, we get $r=\frac{C}{2\pi}$. Substituting $C = 37.7$ inches, $r=\frac{37.7}{2\pi}$. Using $\pi\approx3.14$, $r=\frac{37.7}{2\times3.14}=\frac{37.7}{6.28}\approx6$ inches.

Step3: Find circumference of mountain - bike wheel

The child's bicycle wheel circumference is 50% of the mountain - bike wheel circumference. Let $C_m$ be the mountain - bike wheel circumference. Then $37.7 = 0.5C_m$, so $C_m=\frac{37.7}{0.5}=75.4$ inches.

Step4: Find radius of mountain - bike wheel

Using $r=\frac{C}{2\pi}$ again with $C = 75.4$ inches, $r=\frac{75.4}{2\pi}=\frac{75.4}{2\times3.14}=\frac{75.4}{6.28}=12$ inches.

Answer:

C. 6 in; 12 in