Question

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.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{cuboid}=6y^2, \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2x^2\times \mathrm{Breadth}=2x^2\times 6y^2=12x^2{y}^2\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cuboid}=\frac{3}{2}xy\times \mathrm{Length}=\frac{3}{2}xy\times 12x^2{y}^2=18x^3{y}^3 \\ \mathrm{Now},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cuboid}=\mathrm{Length}\times \mathrm{Breadth}\times \mathrm{Height} \\ =12x^2{y}^2\times 6y^2\times 18x^3{y}^3 \\ =\left(12\times 6\times 18\right)\times \left(x^2\times x^3\right)\times \left(y^2\times y^2\times y^3\right) \\ =1296x^5{y}^7 \end{gathered}$$

Disclaimer: The asnwer given in the textbook is incorrect. The same has been corrected here.