Question

circles end - of - lesson test
6 if the radius of a circle with an area of 125 mm squared is reduced by half, what is the area of the new circle?
41.6 mm squared
62.5 mm squared
31.25 mm squared
250 mm squared
skip 5/10 complete

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Let the original radius be $r_1$ and the new radius be $r_2$. Given $A_1=\pi r_1^{2}=125$ $mm^{2}$, and $r_2=\frac{1}{2}r_1$.

Step2: Find the new - area formula

The new area $A_2=\pi r_2^{2}$. Substitute $r_2 = \frac{1}{2}r_1$ into the formula: $A_2=\pi(\frac{1}{2}r_1)^{2}=\frac{1}{4}\pi r_1^{2}$.

Step3: Substitute the original area value

Since $\pi r_1^{2}=125$ $mm^{2}$, then $A_2=\frac{1}{4}\times125 = 31.25$ $mm^{2}$.

Answer:

31.25 mm squared