In circle [tex]\(G\)[/tex], [tex]\(r = 3\)[/tex] units. Maria draws a circle with double the area of circle [tex]\(G\)[/tex].

What is the area of Maria's circle?

A. [tex]\(6\pi\)[/tex] units[tex]\(^2\)[/tex]
B. [tex]\(9\pi\)[/tex] units[tex]\(^2\)[/tex]
C. [tex]\(12\pi\)[/tex] units[tex]\(^2\)[/tex]
D. [tex]\(18\pi\)[/tex] units[tex]\(^2\)[/tex]



Answer :

Alright, let's solve the problem step by step.

1. Find the area of Circle G:
- Circle G has a radius [tex]\( r = 3 \)[/tex] units.
- The formula to calculate the area of a circle is [tex]\( \text{Area} = \pi r^2 \)[/tex].
- Plugging the radius into the formula, we get:
[tex]\[ \text{Area of Circle G} = \pi \times (3^2) = 9\pi \text{ units}^2 \][/tex]
Thus, the area of Circle G is [tex]\( 9\pi \text{ units}^2 \)[/tex].

2. Find the area of Maria's circle:
- The area of Maria's circle is double the area of Circle G.
- Therefore, we need to multiply the area of Circle G by 2:
[tex]\[ \text{Area of Maria's Circle} = 2 \times (9\pi \text{ units}^2) = 18\pi \text{ units}^2 \][/tex]

Thus, the area of Maria's circle is [tex]\( 18\pi \text{ units}^2 \)[/tex].

Therefore, the correct answer is [tex]\( 18\pi \text{ units}^2 \)[/tex].

So, you should mark the option:
- [tex]\( \bold{18\pi \text{ units}^2} \)[/tex]