Find the volume, lateral surface area and the total surface area of a cube each of whose edges measures:

Solution:

(i) Length of the edge of the cube $=a=7 \mathrm{~m}$

Now, we have the following:

Volume $=a^{3}=7^{3}=343 \mathrm{~m}^{3}$

Lateral surface area $=4 a^{2}=4 \times 7 \times 7=196 \mathrm{~m}^{2}$

Total Surface area $=6 a^{2}=6 \times 7 \times 7=294 \mathrm{~m}^{2}$

(ii) Length of the edge of the cube $=\mathrm{a}=5.6 \mathrm{~cm}$

Now, we have the following:

Volume $=a^{3}=5.6^{3}=175.616 \mathrm{~cm}^{3}$

Lateral surface area $=4 a^{2}=4 \times 5.6 \times 5.6=125.44 \mathrm{~cm}^{2}$

Total Surface area $=6 a^{2}=6 \times 5.6 \times 5.6=188.16 \mathrm{~cm}^{2}$

(iii) Length of the edge of the cube $=\mathrm{a}=8 \mathrm{dm} 5 \mathrm{~cm}=85 \mathrm{~cm}$

Now, we have the following:

Volume $=a^{3}=85^{3}=614125 \mathrm{~cm}^{3}$

Lateral surface area $=4 a^{2}=4 \times 85 \times 85=28900 \mathrm{~cm}^{2}$

Total Surface area $=6 a^{2}=6 \times 85 \times 85=43350 \mathrm{~cm}^{2}$