a figure skater must trace a figure eight on the ice that consists of two perfect circles, each with radius 11 feet. How far does the skater go one time around the figure eight?
Circumference of a circle:
C = pi * d
C = 3.14 * 22
C = ?
To find the distance the skater covers one time around the figure eight, we need to calculate the circumference of each circle and add them together.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Given that the radius of each circle is 11 feet, let's calculate the circumference of one circle:
C1 = 2π * 11
C1 ≈ 2 * 3.14 * 11
C1 ≈ 69.08 feet
Since the skater traces two circles to form the figure eight, the total distance covered is the sum of the circumference of both circles:
Total Distance = C1 + C1
Total Distance = 69.08 + 69.08
Total Distance ≈ 138.16 feet
Therefore, the skater covers approximately 138.16 feet one time around the figure eight.
To find the distance the skater goes one time around the figure eight, we need to calculate the circumference of each circle and multiply it by 2, since there are two circles in the figure eight.
1. Calculate the circumference of a circle:
Circumference = 2 * π * radius
Given that the radius of each circle is 11 feet:
Circumference = 2 * π * 11
2. Calculate the total distance for one circle:
Circle Distance = Circumference
3. Calculate the total distance for the figure eight:
Figure Eight Distance = 2 * Circle Distance
Now, let's substitute the values and calculate the distance:
Circumference = 2 * π * 11
= 22π
Circle Distance = 22π feet
Figure Eight Distance = 2 * Circle Distance
= 2 * 22π
= 44π feet
Therefore, the skater goes a distance of 44π feet one time around the figure eight.