Question

The length,breadth and height of a cuboid are in the ratio 3 2 1. If it's volume is 48 cu cm,find its total surface area.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{breadrh}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{cuboid}\mathrm{be}3\mathrm{x}\mathrm{cm},2\mathrm{x}\mathrm{cm}\mathrm{and}\mathrm{x}\mathrm{cm} \\ \mathrm{Now},\mathrm{volume}\mathrm{of}\mathrm{cuboid}=48{\mathrm{cm}}^3 \\ \Rightarrow \mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=48 \\ \Rightarrow 3\mathrm{x}\times 2\mathrm{x}\times \mathrm{x}=48 \\ \Rightarrow 6{\mathrm{x}}^3=48 \\ \Rightarrow {\mathrm{x}}^3=8 \\ \Rightarrow \mathrm{x}=2 \\ \mathrm{So},\mathrm{length}=3\mathrm{x}=3\times 2=6\mathrm{cm} \\ \mathrm{breadth}=2\mathrm{x}=2\times 2=4\mathrm{cm} \\ \mathrm{height}=\mathrm{x}=2\mathrm{cm} \\ \mathrm{TSA}=2\left[\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{height}\times \mathrm{length}\right] \\ =2\left[6\times 4+4\times 2+2\times 6\right] \\ =2\left[24+8+12\right] \\ =2\times 44 \\ =88{\mathrm{cm}}^2 \end{gathered}$$