Answer :
To find the area of the circle given the circumference, first, we need to figure out the radius of the circle, and then we can use the radius to calculate the area. Let's start by recalling the formulae related to a circle:
1. The circumference (C) of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. The area (A) of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Given that the circumference [tex]\( C = 11\pi \)[/tex] cm, let's solve for the radius ([tex]\( r \)[/tex]):
[tex]\[ 11\pi = 2\pi r \][/tex]
[tex]\[ r = \frac{11\pi}{2\pi} \][/tex]
[tex]\[ r = \frac{11}{2} \][/tex]
[tex]\[ r = 5.5 \][/tex] cm
Now that we have the radius, we can plug it into the formula for the area of the circle:
[tex]\[ A = \pi r^2 \][/tex]
[tex]\[ A = \pi (5.5)^2 \][/tex]
[tex]\[ A = \pi (5.5 \times 5.5) \][/tex]
[tex]\[ A = \pi (30.25) \][/tex]
[tex]\[ A = 30.25\pi \][/tex]
So, the area of the circle is [tex]\( 30.25\pi \)[/tex] square centimeters, expressed in terms of [tex]\(\pi\)[/tex].
1. The circumference (C) of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. The area (A) of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Given that the circumference [tex]\( C = 11\pi \)[/tex] cm, let's solve for the radius ([tex]\( r \)[/tex]):
[tex]\[ 11\pi = 2\pi r \][/tex]
[tex]\[ r = \frac{11\pi}{2\pi} \][/tex]
[tex]\[ r = \frac{11}{2} \][/tex]
[tex]\[ r = 5.5 \][/tex] cm
Now that we have the radius, we can plug it into the formula for the area of the circle:
[tex]\[ A = \pi r^2 \][/tex]
[tex]\[ A = \pi (5.5)^2 \][/tex]
[tex]\[ A = \pi (5.5 \times 5.5) \][/tex]
[tex]\[ A = \pi (30.25) \][/tex]
[tex]\[ A = 30.25\pi \][/tex]
So, the area of the circle is [tex]\( 30.25\pi \)[/tex] square centimeters, expressed in terms of [tex]\(\pi\)[/tex].
