Quantitative Aptitude Ques 1025
Question: The sum of radii of two spheres is 10 cm and the sum of their volumes is $ 880cm^{3}. $ What will be the product of their radii?
Options:
A) $ 21 $
B) $ 26\frac{1}{3} $
C) $ 33\frac{1}{3} $
D) $ 70 $
Show Answer
Answer:
Correct Answer: B
Solution:
- Let $ r _1 $ and $ r _2 $ be the radii of sphere. Given, $ r _1+r _2=10 $ (i) and volume = 880
$ \Rightarrow $ $ \frac{4}{3}\pi (r_1^{3}+r_2^{3})=880 $
$ \Rightarrow $ $ r_1^{3}+r_2^{3}=\frac{880\times 3\times 7}{22\times 4}=210 $ (ii) On cubing both sides of Eq. (i), we get $ {{(r _1+r _2)}^{3}}=1000 $
$ \Rightarrow $ $ r_1^{3}+r_2^{3}+3r _1r _2(r _1+r _2)=1000 $
$ \Rightarrow $ $ 210+3r _1r _2(10)=1000 $
$ \Rightarrow $ $ 30r _1r _2=1000-210=790 $
$ \Rightarrow $ $ r _1r _2=\frac{790}{30}=\frac{79}{3}=26\frac{1}{3} $
BETA
