A parallelopiped whose sides are in ration 2 : 4 : 8 has the same volume as a cube. The ratio of their surface areas is: ?->(Show Answer!)

1. A parallelopiped whose sides are in ration 2 : 4 : 8 has the same volume as a cube. The ratio of their surface areas is:

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By: anil on 05 May 2019 01.42 am

Let length of parallelopiped = $$2x$$ units
Breadth = $$4x$$ units and height = $$8x$$ units Let side of cube = $$a$$ units Acc. to ques, volume of cube = volume of parallelopiped => $$a^3 = 2x imes 4x imes 8x$$ => $$a^3 = 64 x^3$$ => $$a = sqrt[3]{64x} = 4x$$ units Now, surface area of parallelopiped = $$2 (lb + bh + hl)$$ = $$2 (8x^2 + 32x^2 + 16x^2)$$ = $$2 imes 56 x^2 = 112x^2$$ sq. units Surface area of cube = $$6 a^2$$ = $$6 (4x)^2 = 96x^2$$ $$ herefore$$ Required ratio = $$frac{112 x^2}{96 x^2}$$ = $$7 : 6$$

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MCQ-> Since World War II, the nation-state has been regarded with approval by every political system and every ideology. In the name of modernisation in the West, of socialism in the Eastern bloc, and of development in the Third World, it was expected to guarantee the happiness of individuals as citizens and of peoples as societies. However, the state today appears to have broken down in many parts of the world. It has failed to guarantee either security or social justice, and has been unable to prevent either international wars or civil wars. Disturbed by the claims of communities within it, the nation-state tries to repress their demands and to proclaim itself as the only guarantor of security of all. 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The assertion of identity then starts turning into self-absorption and isolation, and is liable to slide into intolerance of others and towards ideas of "ethnic cleansing", xenophobia and violence.Whereas continuous variations among peoples prevent drawing of clear dividing lines between the groups, those militating for recognition of their group's identity arbitrarily choose a limited number of criteria such as religion, language, skin colour, and place of origin so that their members recognise themselves primarily in terms of the labels attached to the group whose existence is being asserted. This distinction between the group in question and other groups is established by simplifying the feature selected. Simplification also works by transforming groups into essences, abstractions endowed with the capacity to remain unchanged through time. 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MCQ-> Read the passage carefully and answer the questions given at the end of each passage:We now come to the second part of our journey under the sea. The first ended with the moving scene in the coral cemetery which left a deep impression on my mind. I could no longer content myself with the theory which satisfied Conseil. That worthy fellow persisted in seeing in the Commander of the Nautilus one of those unknown servants who returns mankind contempt for indifference. For him, he was a misunderstood genius who, tired of earth’s deceptions, had taken refuge in this inaccessible medium, where he might follow his instincts freely. To my mind, this explains but one side of Captain Nemo’s character. Indeed, the mystery of that last night during which we had been chained in prison, the sleep, and the precaution so violently taken by the Captain of snatching from my eyes the glass I had raised to sweep the horizon, the mortal wound of the man, due to an unaccountable shock of the Nautilus, all put me on a new track. No; Captain Nemo was not satisfied with shunning man. His formidable apparatus not only suited his instinct of freedom, but perhaps also the design of some terrible retaliation. That day, at noon, the second officer came to take the altitude of the sun. I mounted the platform, and watched the operation. As he was taking observations with the sextant, one of the sailors of the Nautilus (the strong man who had accompanied us on our first submarine excursion to the Island of Crespo) came to clean the glasses of the lantern. I examined the fittings of the apparatus, the strength of which was increased a hundredfold by lenticular rings, placed similar to those in a lighthouse, and which projected their brilliance in a horizontal plane. The electric lamp was combined in such a way as to give its most powerful light. Indeed, it was produced in vacuo, which insured both its steadiness and its intensity. This vacuum economized the graphite points between which the luminous arc was developed - an important point of economy for Captain Nemo, who could not easily have replaced them; and under these conditions their waste was imperceptible. When the Nautilus was ready to continue its submarine journey, I went down to the saloon. The panel was closed, and the course marked direct west. We were furrowing the waters of the Indian Ocean, a vast liquid plain, with a surface of 1,200,000,000 of acres, and whose waters are so clear and transparent that any one leaning over them would turn giddy. 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