Answer :
To find the area of a circle, we use the formula:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to [tex]\( 3.14159 \)[/tex], and [tex]\( r \)[/tex] is the radius of the circle.
In this case, the radius [tex]\( r \)[/tex] is given as [tex]\( 11 \)[/tex] meters. Plugging this value into the formula, we have:
[tex]\[ A = \pi \times (11)^2 \][/tex]
First, compute the square of the radius:
[tex]\[ 11^2 = 121 \][/tex]
Now, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ A = \pi \times 121 \][/tex]
Using the approximate value of [tex]\( \pi \)[/tex]:
[tex]\[ A \approx 3.14159 \times 121 \][/tex]
[tex]\[ A \approx 380.132711084365 \][/tex]
So, the approximate area of the circle with a radius of 11 meters is [tex]\( 380.132711084365 \)[/tex] square meters. Given the options:
A. [tex]\( 34.5 \, m^2 \)[/tex]
B. [tex]\( 69 \, m^2 \)[/tex]
C. [tex]\( 380 \, m^2 \)[/tex]
D. [tex]\( 190 \, m^2 \)[/tex]
The closest and most accurate option is:
C. [tex]\( 380 \, m^2 \)[/tex]
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to [tex]\( 3.14159 \)[/tex], and [tex]\( r \)[/tex] is the radius of the circle.
In this case, the radius [tex]\( r \)[/tex] is given as [tex]\( 11 \)[/tex] meters. Plugging this value into the formula, we have:
[tex]\[ A = \pi \times (11)^2 \][/tex]
First, compute the square of the radius:
[tex]\[ 11^2 = 121 \][/tex]
Now, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ A = \pi \times 121 \][/tex]
Using the approximate value of [tex]\( \pi \)[/tex]:
[tex]\[ A \approx 3.14159 \times 121 \][/tex]
[tex]\[ A \approx 380.132711084365 \][/tex]
So, the approximate area of the circle with a radius of 11 meters is [tex]\( 380.132711084365 \)[/tex] square meters. Given the options:
A. [tex]\( 34.5 \, m^2 \)[/tex]
B. [tex]\( 69 \, m^2 \)[/tex]
C. [tex]\( 380 \, m^2 \)[/tex]
D. [tex]\( 190 \, m^2 \)[/tex]
The closest and most accurate option is:
C. [tex]\( 380 \, m^2 \)[/tex]
