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# The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is 2x2 times its breadth and the height is $\frac{3}{2}$xy times of length. Find the volume of the cuboid if its breadth is 6y2.

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## $\mathrm{We}\mathrm{have},\phantom{\rule{0ex}{0ex}}\mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{cuboid}=6{y}^{2},\phantom{\rule{0ex}{0ex}}\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2{x}^{2}×\mathrm{Breadth}=2{x}^{2}×6{y}^{2}=12{x}^{2}{y}^{2}\mathrm{and}\phantom{\rule{0ex}{0ex}}\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cuboid}=\frac{3}{2}xy×\mathrm{Length}=\frac{3}{2}xy×12{x}^{2}{y}^{2}=18{x}^{3}{y}^{3}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Now},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cuboid}=\mathrm{Length}×\mathrm{Breadth}×\mathrm{Height}\phantom{\rule{0ex}{0ex}}=12{x}^{2}{y}^{2}×6{y}^{2}×18{x}^{3}{y}^{3}\phantom{\rule{0ex}{0ex}}=\left(12×6×18\right)×\left({x}^{2}×{x}^{3}\right)×\left({y}^{2}×{y}^{2}×{y}^{3}\right)\phantom{\rule{0ex}{0ex}}=1296{x}^{5}{y}^{7}$ Disclaimer: The asnwer given in the textbook is incorrect. The same has been corrected here.  Suggest Corrections  4      Similar questions  Related Videos   Introduction
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