What will happen to the circumference and the area of the maze a fun house maze that is circular in shape has a diameter of 50 feet. the owner decides to double the radius of the maze?
50 / 2 = ?
25times 25= 3.14times25times25
Circumference = pi*2r = pi*Dia. =
3.14 * 50 = 157.1 Ft.
When the radius is doubled, the diameter is also doubled. Therefore, the
Circumference is doubled:
Circumference = 3.14 * 100 = 314.2 Ft.
Area = pi*r^2
When the radius is doubled:
Area = pi * (2r)^2 = pi * 4r^2.
Therefore, the area is 4 times the original value.
A fun house maze that is circular in shape has a diameter of 50 feet. The owner decides to double the radius of the maze. What will happen to the circumference and the area of the maze?
To determine what will happen to the circumference and the area of the maze when the radius is doubled, we need to understand the relationship between the radius, circumference, and area of a circle.
1. Circumference of a Circle: The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius.
2. Area of a Circle: The area of a circle can be calculated using the formula:
A = πr²
where A is the area and r is the radius.
Now, let's calculate the circumference and the area of the initial maze with a diameter of 50 feet (radius = 25 feet):
1. Circumference of initial maze:
C = 2πr
C = 2π(25)
C ≈ 2 * 3.14 * 25
C ≈ 157 feet
2. Area of initial maze:
A = πr²
A = 3.14(25)²
A ≈ 3.14 * 625
A ≈ 1962.5 square feet
Next, let's calculate the circumference and the area when the radius is doubled:
1. New radius:
initial radius = 25 feet
doubled radius = 2 * initial radius = 2 * 25 = 50 feet
2. Circumference of the maze with the doubled radius:
C = 2πr
C = 2π(50)
C ≈ 2 * 3.14 * 50
C ≈ 314 feet
3. Area of the maze with the doubled radius:
A = πr²
A = 3.14(50)²
A ≈ 3.14 * 2500
A ≈ 7850 square feet
In conclusion, when the radius of the maze is doubled, the circumference increases from approximately 157 feet to 314 feet, and the area increases from approximately 1962.5 square feet to 7850 square feet.