Question

lesson 6: circles
changes in dimensions
if the radius of a circle with an area of 12.56 mm squared is multiplied by 5, what is the area of the new circle?
a. 39.43 mm squared
b. 314 mm squared
c. 62.8 mm squared
d. 78.5 mm squared
check answer

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given the initial area $A_1=\pi r_1^{2}=12.56$ mm².

Step2: Analyze the new - radius

The new radius $r_2 = 5r_1$.

Step3: Calculate the new area

The new area $A_2=\pi r_2^{2}=\pi(5r_1)^{2}=25\pi r_1^{2}$. Since $\pi r_1^{2}=12.56$ mm², then $A_2 = 25\times12.56=314$ mm².

Answer:

B. 314 mm squared