Question

circles end - of - lesson test
7 if the diameter of a circle with a circumference of 22.50 inches is reduced by half, what would be the circumference of the new circle?
45 in
3.58 in
35.325 in
11.25 in
skip 6/10 complete

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = \pi d$, where $C$ is the circumference and $d$ is the diameter.

Step2: Analyze the change in diameter

Given the original circumference $C_1=\pi d_1 = 22.50$ inches. The new diameter $d_2=\frac{d_1}{2}$.

Step3: Calculate the new circumference

The new circumference $C_2=\pi d_2$. Substitute $d_2=\frac{d_1}{2}$ into the formula, we get $C_2=\pi\times\frac{d_1}{2}=\frac{1}{2}\times(\pi d_1)$. Since $\pi d_1 = 22.50$ inches, then $C_2=\frac{22.50}{2}=11.25$ inches.

Answer:

11.25 in