Question

Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _AREA RELATED TO CIRCLES

Answer 1

Answer:

$Difference \:major \:\\and minor \:sector \:areas (A)\\ =462\: cm^{2}$

Step-by-step explanation:

Given Radius of the circle (r) = 21cm

/*We know that,

$\boxed {Area \:of\:a \: sector\\=\frac{x\degree}{360\degree }\times \pi r^{2}}$

i ) Sector angle of a minor sector (x) = 120°

ii)Sector angle of the major sector(X) = (360°-120°) = 240°

Now,

$Difference\:of \: the \: sector \: Areas(A) \\= \:Major \:sector\: Area - Minor \:sector \:area \\=\frac{X}{360}\pi r^{2}-\frac{x}{120}\pi r^{2}\\=\frac{\pi r^{2}}{360}\times (X-x)\\=\frac{\pi r^{2}}{360}\times (240-120)\\=\frac{\pi r^{2}}{360}\times 120\\=\frac{22}{7}\times (21)^{2}\times \frac{120}{360}$

After cancellation, we get

$A = 22\times 21$

$A = 462 \:cm^{2}$

Therefore,

$Difference\: of \:the\: areas (A)\\ =462\: cm^{2}$

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Answer 2

Answer:

Step-by-step explanation:

Given Radius of the circle (r) = 21cm

/*We know that,

i ) Sector angle of a minor sector (x) = 120°

ii)Sector angle of the major sector(X) = (360°-120°) = 240°

Now,

After cancellation, we get

$A = 462 \:cm^{2}$

Therefore,

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