SATHEE: Quantitative Aptitude Ques 2194

Quantitative Aptitude Ques 2194

Question: If the chords AP and AQ of a circle of radius 6 cm are at distance 3 cm and $ 3\sqrt{2},cm $ respectively from the centre O of the circle, then the area of the smaller sector POQ is

Options:

A) $ 24,\pi cm^{2} $

B) $ 21,\pi cm^{2} $

C) $ 15,\pi cm^{2} $

D) $ 12,\pi cm^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

In $ \Delta AMO, $ $ \sin \theta =\frac{3}{6} $
$ \Rightarrow $ $ \sin \theta =\frac{1}{2} $ $ \sin \theta =\sin 30{}^\circ $ $ \theta =30{}^\circ $ (i) Similarly, in $ \Delta ANO, $ $ \sin \alpha =\frac{3\sqrt{2}}{6} $
$ \Rightarrow $ $ \sin \alpha =\frac{1}{\sqrt{2}} $

$ \Rightarrow $ $ \alpha =45{}^\circ $

$ \therefore $ $ (\theta +\alpha )=75{}^\circ $ Again $ \angle POQ=2,\angle PAQ $ $ [\because \angle PAQ=75{}^\circ ] $ $ =2\times 75{}^\circ =150{}^\circ $ Area of sector $ POQ=\frac{150}{360}\times \pi \times 36=15\pi ,cm^{2} $

Quantitative Aptitude Ques 2193

Quantitative Aptitude Ques 2195

Quantitative Aptitude Ques 2194

Question: If the chords AP and AQ of a circle of radius 6 cm are at distance 3 cm and $ 3\sqrt{2},cm $ respectively from the centre O of the circle, then the area of the smaller sector POQ is

Options:

Answer:

Solution:

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