Mathematics 10 — Exercise 9.2 · Q9 (i)

Full question

Arc length 11/2 cm, angle 40°20′. Find the radius.

Step-by-step solution

1. Convert minutes to degrees: 20′=20/60°=1/3°. Therefore 40°20′=121/3°.

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

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

   $$\frac{121\times 1}{1\times 270}$$

4. Calculate these two products separately.

   $$\frac{121}{270}$$

5. Calculate this operation before combining the remaining terms.

   $$121\times \frac{1}{270}=\frac{121}{270}$$

6. Calculate this operation before combining the remaining terms.

   $$\frac{1}{\frac{121}{270}\times \pi }=\frac{270}{121\times \pi }$$

7. Calculate this operation before combining the remaining terms.

   $$11\times \frac{270}{121\times \pi }=\frac{270}{11\times \pi }$$

8. Substitute the given numbers into the formula.

   $$\frac{11}{\frac{121}{270}\times \pi }$$

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

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

10. Calculate these two products separately.

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

11. Calculate this operation before combining the remaining terms.

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

12. Calculate this operation before combining the remaining terms.

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

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

    $$\frac{121\times 1}{1\times 3}$$

14. Calculate these two products separately.

    $$\frac{121}{3}$$

15. Calculate this operation before combining the remaining terms.

    $$121\times \frac{1}{3}=\frac{121}{3}$$

16. Calculate this operation before combining the remaining terms.

    $$\frac{121}{3}\times \frac{1}{180}\times \pi =\frac{121}{540}\times \pi$$

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

    $$\frac{121\times 1}{1\times 540}$$

18. Calculate these two products separately.

    $$\frac{121}{540}$$

19. Calculate this operation before combining the remaining terms.

    $$121\times \frac{1}{540}=\frac{121}{540}$$

20. Calculate this operation before combining the remaining terms.

    $$1\times \frac{540}{121\times \pi }=\frac{540}{121\times \pi }$$

21. Calculate this operation before combining the remaining terms.

    $$\frac{1}{\frac{121}{540}\times \pi }=\frac{540}{121\times \pi }$$

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

    $$\frac{11\times 1}{1\times 2}$$

23. Calculate these two products separately.

    $$\frac{11}{2}$$

24. Calculate this operation before combining the remaining terms.

    $$11\times \frac{1}{2}=\frac{11}{2}$$

25. Calculate this operation before combining the remaining terms.

    $$\frac{1}{121\times \pi }=\frac{1}{121\times \pi }$$

26. Calculate this operation before combining the remaining terms.

    $$540\times \frac{1}{121\times \pi }=\frac{540}{121\times \pi }$$

27. Calculate this operation before combining the remaining terms.

    $$\frac{11}{2}\times \frac{540}{121\times \pi }=\frac{270}{11\times \pi }$$

28. Calculate this operation before combining the remaining terms.

    $$\frac{1}{11\times \pi }=\frac{1}{11\times \pi }$$

29. Calculate this operation before combining the remaining terms.

    $$270\times \frac{1}{11\times \pi }=\frac{270}{11\times \pi }$$

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

    $$\frac{270}{11\times \pi }$$

Answer

The final answer is shown below.