Question

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures (a) 9 m, (b) 6.5 cm.

Answer 1

(a) 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 = $4a^2=4\times 9^2{\mathrm{m}}^2=4\times 81{\mathrm{m}}^2=324{\mathrm{m}}^2$
Total surface area of the cube = $6a^2=6\times 9^2{\mathrm{m}}^2=6\times 81{\mathrm{m}}^2=486{\mathrm{m}}^2$
∴ Diagonal of the cube = $\sqrt{3}a=\sqrt{3}\times 9=15.57\mathrm{m}$

(b) Here, a = 6.5 cm

Volume of the cube = $a^3=6.5^3{\mathrm{cm}}^3=274.625{\mathrm{cm}}^3$
Lateral surface area of the cube = $4a^2=4\times 6.5^2{\mathrm{cm}}^2=169{\mathrm{cm}}^2$
Total surface area of the cube = $6a^2=6\times 6.5^2{\mathrm{cm}}^2=253.5{\mathrm{cm}}^2$
∴ Diagonal of the cube = $\sqrt{3}a\mathrm{cm}=\sqrt{3}\times 6.5\mathrm{cm}=11.245\mathrm{cm}$