Quantitative Aptitude Ques 1041
Question: There are two circles of radii $ r _1 $ and $ r _2(r _1<r _2). $ The area of the bigger circle is $ \frac{693}{2}cm^{2}. $ The difference of their circumferences is $ 22cm. $ What is the sum of the diameters of the two circles?
Options:
A) 17.5 cm
B) 22 cm
C) 28.5 cm
D) 35 cm
Show Answer
Answer:
Correct Answer: C
Solution:
- According to the question,
$ \pi r_2^{2}=\frac{693}{2} $
$ \Rightarrow $ $ r_2^{2}=\frac{693}{2}\times \frac{7}{22} $
$ \Rightarrow $ $ r _2=\sqrt{\frac{693\times 7}{2\times 22}} $
$ \therefore $ $ d _2=2\sqrt{\frac{693\times 7}{2\times 22}}=21cm $ Again, according to the question, $ 2\pi r _2-2\pi r _1=22 $
$ \Rightarrow $ $ \pi \times 21-2\pi r _1=22 $
$ \Rightarrow $ $ \frac{22}{7}\times 21-2\pi r _1=22 $
$ \Rightarrow $ $ 66-2\pi r _1=22 $
$ \Rightarrow $ $ 2\pi r _1=44 $
$ \Rightarrow $ $ 2\times \frac{22}{7}\times r _1=44 $
$ r _1=7cm $
$ \therefore $ $ d _1=14cm $
$ \therefore $ $ d _1+d _2=14+21=35cm $
BETA
