Question

Question) if the surface area of a cube is 1176 cm² , find :
(i) the length of a diagonal
(ii) volume of the cube

Answer 1

Dear student
$$\begin{gathered} \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{cube}=1176{\mathrm{cm}}^2 \\ \Rightarrow 6{\mathrm{a}}^2=1176 \\ \Rightarrow {\mathrm{a}}^2=196 \\ \Rightarrow \mathrm{a}=14\mathrm{cm} \\ \mathrm{i})\mathrm{Diagonal}\mathrm{of}\mathrm{cube}=\sqrt{3}\mathrm{a}=\sqrt{3}\times 14=14\sqrt{3}\mathrm{cm} \\ \mathrm{ii})\mathrm{Volume}\mathrm{of}\mathrm{cube}={\mathrm{a}}^3={14}^3=2744{\mathrm{cm}}^3 \end{gathered}$$
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