What is the length of XPY in terms of π?

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a. 192π m
b. 8π m
c. 48π m
d. 24π m

1 answer

The length of XPY can be found using the Pythagorean Theorem:

XP² + PY² = XY²

Plugging in the given values:

(6π)² + (16π)² = XY²
36π² + 256π² = XY²
292π² = XY²

Taking the square root of both sides:

XY = √(292π²)
XY = 2π√73

Since XPY is half of the circle with radius XY, its length is:

XPY = (1/2)(2πr) = πr

Plugging in the value of XY:

XPY = π(2π√73)
XPY = 2π²√73

Therefore, the length of XPY in terms of π is 2π²√73, which is closest to choice a) 192π m.