Quantitative Aptitude Ques 877
Question: A parallelepiped whose sides are in ratio 2: 4: 8 have the same volume as a cube. The ratio of their surface area is
Options:
A) 7 : 5
B) 4 : 3
C) 8 : 5
D) 7 : 6
Show Answer
Answer:
Correct Answer: D
Solution:
- Let the sides of the parallelepiped be 2x, 4x and 8x units, respectively and the edge of cube be a units. According to the question, $ 2x\times 4x\times 8x=a^{3} $
$ \Rightarrow $ $ 8\times 8x^{3}=a^{3} $ Taking cube roots, $ 4x=a $ … (i) Surface area of parallelepiped $ =2(lb+bh+hl) $ $ =2(2x\times 4x+4x\times 8x+8x\times 2x) $ $ =2(8x^{2}+32x^{2}+16x^{2}) $ $ =112x^{2}units $ Surface area of cube $ =6a^{2},units $
$ \therefore $ Ratio of surface area of parallelepiped and cube $ =\frac{112x^{2}}{6a^{2}}=\frac{112x^{2}}{6\times 16x^{2}} $ [from Eq. (i)] $ =7/6 $
$ \therefore $ Required ratio = 7: 6
BETA
