One afternoon, a couple walks five-eighths of the way around a circular lake, the radius of which is 1.45 km. They start at the west side of the lake and head due south to begin with.
(a) What is the distance they travel?
distance=radius*5/8*radius*2PI
delete one of the radius in the above, I got carried away.
WHAT IS Pl???
To find the distance the couple travels, we first need to determine the circumference of the circular lake.
The circumference of a circle can be calculated using the formula:
C = 2πr
Where:
C = circumference
π (pi) ≈ 3.14159
r = radius
Given that the radius of the circular lake is 1.45 km, we can substitute this value into the formula:
C = 2π(1.45)
Calculating this expression gives us:
C ≈ 2 * 3.14159 * 1.45
C ≈ 9.094 km
Now, to determine the distance the couple travels, we need to find five-eighths of the circumference.
Fraction of circumference traveled = 5/8
Therefore, the distance traveled by the couple is:
Distance traveled = Fraction of circumference traveled * Circumference
Distance traveled ≈ (5/8) * 9.094
Calculating this gives us:
Distance traveled ≈ (5/8) * 9.094
Distance traveled ≈ 5.68375 km
Therefore, the couple travels approximately 5.68375 km.