Question

9. Area of a circle is 314 cm². If the area of a major sector is 214 cm?, then what is the area of the
corresponding minor sector?
(A) 314 cm
(B) 100 cm?
(C) 114 cm
(D) 214 cm​

Answer 1

Correct Question:

Area of a circle is 314 cm². If the area of a major sector is 214 cm², then what is the area of the corresponding minor sector?

(A) 314 cm

(B) 100 cm²

(C) 114 cm

(D) 214 cm​

SOLUTION:

Given:

• The area of a circle is 314 cm²
• The area of a major sector is 214 cm²

To find:

• The area of the corresponding minor sector.

To get the area of the minor sector, we have to subtract the area of the major sector from the area of the circle.

So,

Area of minor sector = [Area of the circle - Area of the major sector]

Area of the minor sector = [314 - 214]

• [By putting the given values]

Area of the minor sector = 100 cm²

Hence,

• Option (B) 100 cm² is the correct answer.

More information,

The formula to find the area of a sector is $\boxed{\frac{\theta}{360} \pi r^{2}}\ unit\ sq.$

Answer 2

${\large{\bold{\rm{\underline{Correct \; question}}}}}$

★ Area of a circle is 314 cm². If the area of a major sector is 214 cm², then what is the area of the corresponding minor sector?

• (A) 314 cm²
• (B) 100 cm²
• (C) 114 cm²
• (D) 214 cm²

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Area of a circle = 314 cm²

★ The area of a major sector = 214 cm²

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Area of corresponding minor sector

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Area of corresponding minor sector = 100 cm² or Option (B)

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

★ Formula to find area of minor sector.

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

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

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

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

➝ Area of minor sector = 314 - 214

➝ Area of minor sector = 100 cm²

${\large{\bold{\rm{\underline{Additional \; knowledge}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: circle = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Circumference \: of \: circle \: = \: 2 \pi r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$