Question

Find the area of sector, whose radius is 7 cm. with the given angle:
i. 60° ii. 30° iii. 72° iv. 90° v. 120°

Answer 1

Answer :

Area of sector = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

Given, radius = 7 cm

i. 60°

Area = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

$\implies\frac{60^{\circ}}{360^{\circ}}\times\frac{22}{7}\times{7}^{2}$

$\implies 25.66\:cm^{2}$

ii. 30°

Area = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

$\implies\frac{30^{\circ}}{360^{\circ}}\times\frac{22}{7}\times{7}^{2}$

$\implies 12.83\:cm^{2}$

iii. 72°

Area = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

$\implies\frac{72^{\circ}}{360^{\circ}}\times\frac{22}{7}\times{7}^{2}$

$\implies 30.8\:cm^{2}$

iv. 90°

Area = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

$\implies\frac{90^{\circ}}{360^{\circ}}\times\frac{22}{7}\times{7}^{2}$

$\implies 38.5\:cm^{2}$

v. 120°

Area = $\frac{\theta}{360^{\circ}}\times\pi{r}^{2}$

$\implies\frac{120^{\circ}}{360^{\circ}}\times\frac{22}{7}\times{7}^{2}$

$\implies 51.33\:cm^{2}$

Answer 2

Answers :

Given : Radius = 7 cm

_________________________

Solution :

Using the formula for Area of Sector

$\bf {Area \: of \: sector = \frac{ \theta}{360} \times \pi \: r {}^{2}}$

___________________________

1. 60°

Area of sector $\sf { = \frac{60}{360} \times \frac{22}{7} \times 7 \times 7}$

$\sf{= \frac{1}{6} \times 22 \times 7}$

$\sf {\frac{154}{6} =25.6}$

Area of sector whose angle is 60° is 25.6 cm^2.

_____________________________

2. 30°

Area of sector = $\sf{ = \frac{30}{360 } \times \frac{22}{7} \times 7 \times 7}$

$\sf {= \frac{1}{12} \times 22 \times 7}$

$\sf{= \frac{154}{12} = 12.83}$

Area of the sector whose radius is 7 cm is 12.83 sq.cm

____________________________

3. 72°

Area of sector = $\sf{ = \frac{72}{360 } \times \frac{22}{7} \times 7 \times 7}$

$\sf{ = \frac{1}{5} \times 22 \times 7}$

$\sf{ = \frac{154}{5} = 30.8 }$

Hence,

Area of sector whose radius is 7 cm is 30.8 sq.cm

___________________________

4. 90°

Area of sector = $\sf{ = \frac{90}{360 } \times \frac{22}{7} \times 7 \times 7}$

$\sf{= \frac{1} {4} \times 22 \times 7}$

$\sf{= \frac{154}{4} = 38.5}$

Area of sector whose radius is 7 cm is 38.5 sq.cm

_____________________________

5. 120°

Area of sector = $\sf{ = \frac{120}{360 } \times \frac{22}{7} \times 7 \times 7}$

$\sf{ = \frac{1}{3} \times 22 \times 7}$

$\sf {= \frac{154}{3} = 51.3}$

Area of sector whose radius is 7 cm is 51.3 sq.cm.

____________________________

$\huge \sf{Final \: Answers }$

➡️1. 25.6 sq.cm

➡️2. 12.83 sq.cm

➡️3. 30.8 sq.cm

➡️4. 38.5 sq.cm

➡️5. 51.3 sq.cm

___________________________❤️