Question 7 of 10

What is the approximate area of a circle with a radius of [tex][tex]$11 m$[/tex][/tex]?

A. [tex][tex]$34.5 m^2$[/tex][/tex]

B. [tex][tex]$69 m^2$[/tex][/tex]

C. [tex][tex]$380 m^2$[/tex][/tex]

D. [tex][tex]$190 m^2$[/tex][/tex]



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]