Arc Length 37Cf22

1. **State the problem:** We need to find the length of an arc of a circle with radius $7$ cm and central angle $90^\circ$. 2. **Formula for arc length:** The length $L$ of an arc with radius $r$ and central angle $\theta$ (in degrees) is given by: $$L = 2 \pi r \times \frac{\theta}{360}$$ 3. **Substitute the values:** Here, $r = 7$ cm and $\theta = 90^\circ$. Using $\pi = 3.14$ as instructed: $$L = 2 \times 3.14 \times 7 \times \frac{90}{360}$$ 4. **Simplify the fraction:** $$\frac{90}{360} = \frac{1}{4}$$ 5. **Calculate the arc length:** $$L = 2 \times 3.14 \times 7 \times \frac{1}{4}$$ 6. **Multiply step-by-step:** $$2 \times 3.14 = 6.28$$ $$6.28 \times 7 = 43.96$$ $$43.96 \times \frac{1}{4} = \cancel{43.96} \times \frac{1}{\cancel{4}} = 10.99$$ 7. **Final answer:** The length of the $90^\circ$ arc is $10.99$ cm (rounded to 2 decimal places).