Question

the radius of a circle is 14.6 millimeters. what is the circles area? round your answer to the nearest hundredth. square millimeters

Explanation:

Step1: Write 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 \(r = 14.6\) mm. Substitute \(r\) into the formula: \(A=\pi\times(14.6)^{2}\).
First, calculate \((14.6)^{2}=14.6\times14.6 = 213.16\).
Then, \(A=\pi\times213.16\). Taking \(\pi\approx3.14159\), we have \(A\approx3.14159\times213.16\).

Step3: Calculate the value

\(3.14159\times213.16 = 3.14159\times(200 + 13+0.16)=3.14159\times200+3.14159\times13 + 3.14159\times0.16\)
\(=628.318+40.84067+0.5026544\)
\(=669.6613244\approx669.66\) (rounded to the nearest hundredth)

Answer:

\(669.66\) square millimeters