Question

3
Saniya said that the area of sector is 77 cm, whose radius 14 cm
and angle 45°." Do you agree ? Give reason.​

Answer 1

Answer:

yes

Step-by-step explanation:

1÷8×22÷7×14×14=77

Answer 2

Recall:

$\text{Area of a sector } = \dfrac{\theta}{360} \times \pi r^2$

Find the area of a sector with and angle of 45° and a radius of 14 cm:

$\text{Area of a sector } = \dfrac{\theta}{360} \times \pi r^2$

$\text{Area of a sector } = \dfrac{45}{360} \times \dfrac{22}{7} \times (14)^2$

$\text{Area of a sector } = \dfrac{1}{8} \times \dfrac{22}{7} \times \dfrac{196}{1}$

$\text{Area of a sector } = 77 \text{ cm}^2$

$\text {Yes, the sector is 77 cm}^2$

$\underline {\text{Reason:}}$

$\text{Area of the circle whose radius is 14 cm is } \dfrac{22}{7} \times 14^2 = 616 \text{ cm}^2$

$\tex{45}^\circ \text{ of a circle is } \dfrac{45}{360} = \dfrac{1}{8} \text{ of the whole circle. }$

$\dfrac{1}{8} \text{ of the circle is } 616 \div 8 = 77 \text{ cm}^2$