Mathematics 10 — Exercise 9.2 · Q10 (ii), area

Full question

Radius 3 cm, θ=pi/4 radians. Find sector area.

Step-by-step solution

1. Sector area A=½r²θ when θ is in radians.

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

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

3. Calculate these two products separately.

   $$\frac{1}{2}$$

4. Calculate this operation before combining the remaining terms.

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

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.

   $$\frac{1}{2}\times 3^2\times \frac{1}{4}\times \pi$$

9. Calculate this operation before combining the remaining terms.

   $$3^2=9$$

10. Calculate this operation before combining the remaining terms.

    $$\frac{1}{2}\times 9\times \frac{1}{4}\times \pi =\frac{9}{8}\times \pi$$

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

    $$\frac{9\times 1}{1\times 8}$$

12. Calculate these two products separately.

    $$\frac{9}{8}$$

13. Calculate this operation before combining the remaining terms.

    $$9\times \frac{1}{8}=\frac{9}{8}$$

14. The required result is shown below. Unit: cm²

    $$\frac{9}{8}\times \pi$$

Answer

The final answer is shown below.