W. W. Arc length 729 The radius of a circle is 8 miles. What is the length of a $$ 90^{\circ} $$ arc? Give the exact answer in simplest form. $$ \square $$ miles

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We are given a circle with radius $$ r = 8 $$ miles and an arc defined by an angle of $$ 90^{\circ} $$. The arc length $$ s $$ of a circle is given by the formula:

$$
s = \left(\frac{\theta}{360^{\circ}}\right) \times (2\pi r)
$$

Substitute the given values:

1. Calculate the circumference of the circle:

$$
2\pi r = 2\pi(8) = 16\pi
$$

2. Compute the fraction of the circle corresponding to $$ 90^{\circ} $$:

$$
\frac{90^{\circ}}{360^{\circ}} = \frac{1}{4}
$$

3. Multiply the circumference by this fraction to get the arc length:

$$
s = \frac{1}{4}(16\pi) = 4\pi
$$

Thus, the exact length of the $$ 90^{\circ} $$ arc is $$ \boxed{4\pi} $$ miles.
The length of the $$ 90^{\circ} $$ arc is $$ 4\pi $$ miles.

W. W. Arc length 729 The radius of a circle is 8 miles. What is the length of a \( 90^{\circ} \) arc? Give the exact answer in simplest form. \( \square \) miles

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