SATHEE: Quantitative Aptitude Ques 879

Quantitative Aptitude Ques 879

Question: If two adjacent sides of a rectangular parallelepiped are 1 cm and 2 cm and the total surface area of the parallelepiped is $ 22cm^{2}, $ then the diagonal of the parallelepiped is

Options:

A) $ \sqrt{10}cm $

B) $ 2\sqrt{3}cm $

C) $ \sqrt{14}cm $

D) $ 4cm $

Show Answer

Answer:

Correct Answer: C

Solution:

Let the third side of the rectangular parallelepiped be x. Total surface area of parallelepiped $ =22 $

$ \Rightarrow $ $ 2(lb+bh+lh)=22 $

$ \Rightarrow $ $ 2(x\times 1+1\times 2+2\times x)=22 $

$ \Rightarrow $ $ 3x+2=11 $

$ \Rightarrow $ $ 3x=11-2=9 $

$ \Rightarrow $ $ x=\frac{9}{3}=3cm $

$ \therefore $ Diagonal of parallelepiped $ =\sqrt{l^{2}+b^{2}+h^{2}} $ $ =\sqrt{3^{2}+2^{2}+1^{2}} $ $ =\sqrt{9+4+1}=\sqrt{14}cm $

Quantitative Aptitude Ques 878

Quantitative Aptitude Ques 880

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