Question

when isabelle won a contest, she got a bronze medal with a radius of 12 centimeters. what is the medals area? if necessary, round your answer to the nearest hundredth. square centimeters

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Substitute the given radius into the formula

Given \(r = 12\) cm. Substitute \(r = 12\) into \(A=\pi r^{2}\), we get \(A=\pi\times(12)^{2}\).
First, calculate \((12)^{2}=144\). So \(A = 144\pi\).

Step3: Calculate the numerical value

Taking \(\pi\approx3.14159265\), then \(A=144\times3.14159265\).
\(144\times3.14159265 = 452.3893416\).

Step4: Round to the nearest hundredth

Rounding \(452.3893416\) to the nearest hundredth (two - decimal places). The third decimal digit is \(9\), so we round up the second decimal digit. \(452.3893416\approx452.39\).

Answer:

\(452.39\)