Question

the radius of a circle is 19 feet. what is the circle’s area? round your answer to the nearest hundredth. square feet

Explanation:

Step1: Recall the formula for the area of a circle

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

Step2: Substitute the given radius into the formula

Given that the radius \( r = 19 \) feet. Substitute \( r = 19 \) into the formula: \( A=\pi\times(19)^{2} \).
First, calculate \( 19^{2}=19\times19 = 361 \). So, \( A = \pi\times361\approx3.14159\times361 \).

Step3: Calculate the numerical value

\( 3.14159\times361 = 3.14159\times(300 + 60+1)=3.14159\times300+3.14159\times60 + 3.14159\times1=942.477+188.4954+3.14159 = 1134.11399\). Rounding to the nearest hundredth (two decimal places), we look at the third decimal place. The third decimal place is 3, which is less than 5, so we round down. So, \( A\approx1134.11 \).

Answer:

1134.11