A) \[351\,c{{m}^{2}}\]
B) \[256\,c{{m}^{2}}\]
C) \[265\,c{{m}^{2}}\]
D) \[315\,c{{m}^{2}}\]
Correct Answer: A
Solution :
Let length = \[l\], breadth = b, height == h. \[l+b+h=24\] (given) .....(i) Diagonal of parallellopiped= 15 cm \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}=15\] or \[{{l}^{2}}+{{b}^{2}}+{{h}^{2}}=225\] Squaring eqn. (i) on both sides \[{{l}^{2}}+{{b}^{2}}+{{h}^{2}}+2lb+2bh+2hl=576\] \[2(l\,b+bh+hl)=576-225=351\] [\[\because \] Surface area of parallellopiped \[=2(l\,b+bh+hl)\]]
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