SATHEE: Quantitative Aptitude Ques 589

Quantitative Aptitude Ques 589

Question: The ratio of the area of a sector of a circle to the area of the circle is 1: 4. If the area of the circle is $ 154cm^{2}, $ the perimeter of the sector is

Options:

A) 20 cm

B) 25 cm

C) 36 cm

D) 40 cm

Show Answer

Answer:

Correct Answer: B

Solution:

$ \frac{Area,of,sector}{Area,of,circle}=\frac{1}{4} $

$ \Rightarrow $ Area of sector $ =\frac{Area,of,circle}{4} $

$ \Rightarrow $ $ \pi r^{2}( \frac{\theta {}^\circ }{360{}^\circ } )=\frac{\pi r^{2}}{4} $
$ \Rightarrow $ $ \theta {}^\circ =\frac{360{}^\circ }{4}=90{}^\circ $ $ \because $ Area of circle $ =\pi r^{2} $

$ \Rightarrow $ $ 154=\pi r^{2} $

$ \Rightarrow $ $ r^{2}=\frac{154\times 7}{22} $
$ \Rightarrow $ $ r=7 $ Perimeter of sector $ =\frac{2\pi r\theta }{360{}^\circ }+2r=\frac{2\pi r\times 90{}^\circ }{360{}^\circ }+2r $ $ =\frac{\pi r}{2}+2r=\frac{\pi \times 7}{2}+2\times 7 $ $ =11+14=25,cm $

Quantitative Aptitude Ques 588

Quantitative Aptitude Ques 590

Quantitative Aptitude Ques 589

Question: The ratio of the area of a sector of a circle to the area of the circle is 1: 4. If the area of the circle is $ 154cm^{2}, $ the perimeter of the sector is

Options:

Answer:

Solution:

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