Question

find the height and volume of a cuboid if its surface area is 758 cm². And its length and breadth is 14 and 11 cm respectively.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cuboid}=\mathrm{h} \\ \mathrm{Now},\mathrm{length},\mathrm{l}=14\mathrm{cm} \\ \mathrm{Breadth},\mathrm{b}=11\mathrm{cm} \\ \mathrm{Now},\mathrm{TSA}=758{\mathrm{cm}}^2 \\ \Rightarrow 2\left(\mathrm{lb}+\mathrm{bh}+\mathrm{hl}\right)=758 \\ \Rightarrow 14\times 11+11\mathrm{h}+14\mathrm{h}=379 \\ \Rightarrow 25\mathrm{h}=225 \\ \Rightarrow \mathrm{h}=9\mathrm{cm} \\ \mathrm{Now},\mathrm{volume}=\mathrm{lbh}=14\times 11\times 9=1386{\mathrm{cm}}^3 \end{gathered}$$