Question

Find the area of the sector of a circle with radius 4 cm and of the angle 30 o . Also, find the area of the corresponding major sector.

Answer 1

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• Radius of the circle = 4 cm
• Angle measures = 30°

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$

Find the area of major sector and minor sector = ?

$\huge{\underline{\underline{\bf{FORMULA\:USED:-}}}}$

$\large{\boxed{\bf{\red{Area\: of \: Sector = \frac{\theta}{360}\times π{r}^{2}}}}}$

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

Now, We have to find the area of sector

Putting the given values in the formula, we get

Take π = 22/7

$\implies$$\bf{\frac{30}{360}\times \frac{22}{7}\times {(4)}^{2}}$

$\implies$$\bf{\frac{\cancel{30}}{\cancel{360}}\times \frac{22}{7}\times 4 \times \cancel {4}}$

$\implies$$\bf{\cancel\dfrac {88}{21}}$

$\large\bf\red{ Area \: of \: minor\: sector = 4.19\: {cm}^{2}}$

Thus, the area of minor sector is 4.19 cm²

Now, we have to find the area of major sector

Area of major sector = Area of circle – Area of minor sector

$\implies$$\bf{ π{r}^{2} - 4.19}$

$\implies$$\bf{ \frac{22}{7}\times{(4)}^{2} - 4.19}$

$\implies$$\bf{ \cancel\dfrac{352}{7} - 4.19}$

$\implies$$\bf{ 50.28 - 4.19}$

$\implies$$\large\bf\red{ Area \: of \: major\: Sector = 46.09\: {cm}^{2}}$

Thus, the area of major sector is 46.09 cm²

$\large{\underline{\underline{\bf{FINAL\: ANSWER:-}}}}$

$\large{\boxed{\boxed{\bf{\red{Area\: of\: minor \: sector = 4.19\:{cm}^{2}}}}}}$

$\large{\boxed{\boxed{\bf{\red{Area \: of \: major \: sector = 46.09\: {cm}^{2}}}}}}$

Answer 2

Answer:

=> The are of minor sector is 4.19cm².

=> Area of major sector = 46.09cm²

$\large\underline\mathrm{Given:-}$

• Radius of the circle = 4cm
• Area = 30°

$\large\underline\mathrm{To \: find}$

The area of major sector and minor sector?

$\large\underline\mathrm{Solution}$

Area of sector = (theta)/360° × πr²

$\implies$ 30°/360° × 22/7 × (4)²

$\implies$ 30°/360° × 22/7 × 16

$\implies$ 88/21

$\implies$ Area of sector = 4.19cm².

Thus,

The are of minor sector is 4.19cm².

Now, We have the find the are of bmajor sector.

Area of major sector = Area of circle - Area of minor sector.

Area of major sector = πr² - 4.19

$\implies$ 22/7 × 4² - 4.19

$\implies$ 352/7 - 4.19

$\implies$ 50.28 - 4.19

$\implies$ 46.09

Area of major sector = 46.09cm².

Thus,

The area of major sector is 46.09cm².