Question

the tsa of a cube is 32 2/3 m cube . find the volume of the cube.

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{surface}\mathrm{area}=32\frac{2}{3}=\frac{98}{3}\mathrm{m} \\ \mathrm{It}\mathrm{is}\mathrm{known}\mathrm{that},\mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{cube}=6{\mathrm{a}}^2 \\ \mathrm{Here},\mathrm{a}\mathrm{is}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{cube} \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \frac{98}{3}\mathrm{m}=6{\mathrm{a}}^2 \\ \Rightarrow {\mathrm{a}}^2=\frac{98}{18}=\frac{49}{9} \\ \Rightarrow \mathrm{a}=\sqrt{\frac{49}{9}} \\ \Rightarrow \mathrm{a}=\frac{7}{3} \\ \mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{cube}={\mathrm{a}}^3 \\ ={\left(\frac{7}{3}\right)}^3 \\ =\frac{343}{27}{\mathrm{m}}^3 \\ =12.70{\mathrm{m}}^3 \end{gathered}$$