Mathematics 10 — Exercise 9.2 · Q10 (i), arc

Full question

Radius 17/10 cm, θ=1/4 radians. Find arc length.

Step-by-step solution

1. Use l=rθ.

2. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{17\times 1}{1\times 10}$$

3. Calculate these two products separately.

   $$\frac{17}{10}$$

4. Calculate this operation before combining the remaining terms.

   $$17\times \frac{1}{10}=\frac{17}{10}$$

5. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{1\times 1}{1\times 4}$$

6. Calculate these two products separately.

   $$\frac{1}{4}$$

7. Calculate this operation before combining the remaining terms.

   $$1\times \frac{1}{4}=\frac{1}{4}$$

8. Substitute the given numbers into the formula.

   $$\frac{17}{10}\times \frac{1}{4}$$

9. Calculate this operation before combining the remaining terms.

   $$17\times 1=17$$

10. Calculate this operation before combining the remaining terms.

    $$10\times 4=40$$

11. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{17\times 1}{1\times 40}$$

12. Calculate this operation before combining the remaining terms.

    $$17\times \frac{1}{40}=\frac{17}{40}$$

13. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{17\times 1}{10\times 4}$$

14. Calculate these two products separately.

    $$\frac{17}{40}$$

15. Calculate this operation before combining the remaining terms.

    $$\frac{17}{10}\times \frac{1}{4}=\frac{17}{40}$$

16. The required result is shown below. Unit: cm

    $$\frac{17}{40}$$

Answer

The final answer is shown below.