A) \[({{x}^{3}}+3xy+27{{y}^{3}}){{m}^{3}}\]
B) \[({{x}^{4}}+2{{x}^{2}}{{y}^{2}}+81{{y}^{4}}){{m}^{3}}\]
C) \[({{x}^{2}}-81{{y}^{4}}){{m}^{3}}\]
D) \[({{x}^{4}}+81{{y}^{4}}){{m}^{3}}\]
Correct Answer: C
Solution :
Volume of cuboidal tank \[\text{=}\,\text{Length }\!\!\times\!\!\text{ breadth }\!\!\times\!\!\text{ height}\] \[(x-3y)(x+3y)({{x}^{2}}+9{{y}^{2}})\] \[=({{x}^{2}}-9{{y}^{2}})({{x}^{2}}+9{{y}^{2}})=({{x}^{4}}-81{{y}^{4}}){{m}^{3}}\]
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