Question

circles end - of - lesson test
9 if the diameter of a circle with a circumference of 104.48 mm is reduced by 1/2, what is the circumference of the new circle?
52.24 mm
417.92 mm
6.53 mm
328.16 mm
4 skip 8/10 complete

Explanation:

Step1: Recall 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 diameter change

The original diameter has a circumference $C_1=\pi d_1 = 104.48$ mm. The new diameter $d_2=\frac{1}{2}d_1$.

Step3: Find new - circumference

The new circumference $C_2=\pi d_2$. Substitute $d_2=\frac{1}{2}d_1$ into the formula, we get $C_2=\pi\times\frac{1}{2}d_1=\frac{1}{2}\pi d_1$. Since $C_1 = \pi d_1=104.48$ mm, then $C_2=\frac{1}{2}C_1$.
$C_2=\frac{104.48}{2}=52.24$ mm.

Answer:

52.24 mm