Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m.

Question:

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures $9 \mathrm{~m}$. (Take $\sqrt{3}=1.73$.)

Solution:

Here, a = 9 m

Volume of the cube $=a^{3}=9^{3} \mathrm{~m}^{3}=729 \mathrm{~m}^{3}$

Lateral surface area of the cube $=4 a^{2}=4 \times 9^{2} \mathrm{~m}^{2}=4 \times 81 \mathrm{~m}^{2}=324 \mathrm{~m}^{2}$

Total surface area of the cube $=6 a^{2}=6 \times 9^{2} \mathrm{~m}^{2}=6 \times 81 \mathrm{~m}^{2}=486 \mathrm{~m}^{2}$

$\therefore$ Diagonal of the cube $=\sqrt{3} a=\sqrt{3} \times 9=15.57 \mathrm{~m}$

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