Question

The dimensions of a cuboid are in the ratio 5:3:2. Its volume is 21870 cm cube .find its total surface area.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{cuboid}=5x\mathrm{cm} \\ \mathrm{breadth}\mathrm{of}\mathrm{cuboid}=3x\mathrm{cm} \\ \mathrm{height}\mathrm{of}\mathrm{cuboid}=2x\mathrm{cm} \\ \mathrm{volume}\mathrm{of}\mathrm{cuboid}=21870{\mathrm{cm}}^3 \\ \Rightarrow \mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=21870 \\ \Rightarrow 5x\times 3x\mathit{}\times 2x\mathit{}=21870 \\ \Rightarrow 30x^3=21870 \\ \Rightarrow x^3=729 \\ \Rightarrow x=9 \\ \mathrm{so},\mathrm{length}=45\mathrm{cm} \\ \mathrm{breadth}=27\mathrm{cm} \\ \mathrm{height}=18\mathrm{cm} \\ \mathrm{Now},\mathrm{TSA}=2\left[\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{height}\times \mathrm{length}\right] \\ \mathrm{TSA}=2\left(45\times 27+27\times 18+\times 18\times 45\right)=2\left(1215+486+810\right)=2\times 2511=5022{\mathrm{cm}}^2 \end{gathered}$$