Serena is standing at the center of a room measuring 11m x 20m. She can spin in a circle covering an area of 201.06m^2. Her wand gives her an attack radius of 1m. The area of her total attack range is calculated to be 197.92m^2 by subtracting the area of her wand radius (3.14m^2) from the total area covered by her spin (201.06m^2).

1. Question # 3

2. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack
range. Find the standard form of the circle. Trouble is standing at (5,6)
will Serena hit Trouble?
Lets create a rough sketch, to get a visual.
11m
20m

3. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
5.5
20m
10

4. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
20m
10
5.5
Make this our
coordinate plane so
that the center is a (0,0)

5. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
20m
10
5.5
Make this our
coordinate plane so
that the center is a (0,0)

6. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
10 20m
201.06
= r
pi
r = 8
5.5
Make this our
coordinate plane so
that the center is a (0,0)

7. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
10 20m
201.06
= r
pi
r = 8
5.5
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
Make this our
coordinate plane so
that the center is a (0,0)

8. Serena is standing at the center of a room with the dimensions of 11 m x
2
20 m. She can spin in 360 degrees covering an area of 201.06m . When
she is holding her wand her radius is 1.0 m. Find the area of the attack.
Find the standard form of the circle. Trouble is standing at (x,y) will she
hit it?
Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
10 20m
201.06
= r
pi
r = 8
5.5
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
2
Make this our A= (pi) 1
coordinate plane so
that the center is a (0,0) A= 3.14

9. Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
8 2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
20m
1 201.06
= r
pi
7
r = 8
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
2
Make this our A= (pi) 1
coordinate plane so
that the center is a (0,0) A= 3.14
Area of attack range.
area of spin ­ area of arm and wand = area of attack range
2
201.06 ­ 3.14 = 197.92m

10. Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
8 2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
20m
1 201.06
= r
pi
7
r = 8
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
2
Make this our A= (pi) 1
coordinate plane so
that the center is a (0,0) A= 3.14
Area of attack range. Standard form of the circle
area of spin ­ area of arm and wand = area of attack range 2 2 2
(x ­ h ) + ( y ­ k) = r Center is
2
201.06 ­ 3.14 = 197.92m (h,k) which
is (0, 0).

11. Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
8 2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
20m
1 201.06
= r
pi
7
r = 8
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
2
Make this our A= (pi) 1
coordinate plane so
that the center is a (0,0) A= 3.14
Area of attack range. Standard form of the circle
area of spin ­ area of arm and wand = area of attack range 2 2 2
(x ­ h ) + ( y ­ k) = r Center is
2
201.06 ­ 3.14 = 197.92m (h,k) which
2 2
x + y = 64 is (0, 0).

12. Lets create a rough sketch, to get a visual. Let us find the center of the room.
11m 11 20 10
= 5.5 =
2 2
Let us find the radius of her spin.
8 T 2
Area of a circle = (pi) r
2 Fill in what we know
201.06 = (pi)r and solve for r.
20m
1 201.06
= r
pi
7
r = 8
We also want to find the area she covers with her arm and wand.
2
Area of a circle = (pi) r
2
Make this our A= (pi) 1
coordinate plane so
that the center is a (0,0) A= 3.14
Area of attack range. Standard form of the circle
area of spin ­ area of arm and wand = area of attack range 2 2 2
(x ­ h ) + ( y ­ k) = r Center is
2
201.06 ­ 3.14 = 197.92m (h,k) which
2 2
x + y = 64 is (0, 0).
Trouble is in Serena's attack range and can be hit.

13. Question # 3
Solved!!

14. Attachments
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