Mathematics 10 — Exercise 9.2 · Q9 (ii)

Full question

Arc length 13 cm, angle 70°. Find the radius.

Step-by-step solution

1. The given angle is 70°.

2. Convert degrees to radians by multiplying by π/180. Then use r=l/θ.

3. Substitute the given numbers into the formula.

   $$\frac{13}{70\times \frac{\pi }{180}}$$

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

   $$\frac{1\times 1}{1\times 180}$$

5. Calculate these two products separately.

   $$\frac{1}{180}$$

6. Calculate this operation before combining the remaining terms.

   $$1\times \frac{1}{180}=\frac{1}{180}$$

7. Calculate this operation before combining the remaining terms.

   $$\pi \times \frac{1}{180}=\frac{1}{180}\times \pi$$

8. Calculate this operation before combining the remaining terms.

   $$70\times \frac{1}{180}\times \pi =\frac{7}{18}\times \pi$$

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

   $$\frac{7\times 1}{1\times 18}$$

10. Calculate these two products separately.

    $$\frac{7}{18}$$

11. Calculate this operation before combining the remaining terms.

    $$7\times \frac{1}{18}=\frac{7}{18}$$

12. Calculate this operation before combining the remaining terms.

    $$1\times \frac{18}{7\times \pi }=\frac{18}{7\times \pi }$$

13. Calculate this operation before combining the remaining terms.

    $$\frac{1}{\frac{7}{18}\times \pi }=\frac{18}{7\times \pi }$$

14. Calculate this operation before combining the remaining terms.

    $$\frac{1}{7\times \pi }=\frac{1}{7\times \pi }$$

15. Calculate this operation before combining the remaining terms.

    $$18\times \frac{1}{7\times \pi }=\frac{18}{7\times \pi }$$

16. Calculate this operation before combining the remaining terms.

    $$13\times \frac{18}{7\times \pi }=\frac{234}{7\times \pi }$$

17. Calculate this operation before combining the remaining terms.

    $$234\times \frac{1}{7\times \pi }=\frac{234}{7\times \pi }$$

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

    $$\frac{234}{7\times \pi }$$

Answer

The final answer is shown below.