Question

Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2 m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{Dimension}\mathrm{of}\mathrm{the}\mathrm{cuboid}: \\ \mathrm{Length}=10\mathrm{cm} \\ \mathrm{Breadth}=12\mathrm{cm} \\ \mathrm{Height}=14\mathrm{cm} \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\times (\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{length}\times \mathrm{height}) \\ =2\times (10\times 12+12\times 14+10\times 14) \\ =2\times (120+168+140) \\ =856{\mathrm{cm}}^2 \\ \left(\mathrm{ii}\right) \\ \mathrm{Dimensions}\mathrm{of}\mathrm{the}\mathrm{cuboid}: \\ \mathrm{Length}=6\mathrm{dm} \\ \mathrm{Breadth}=8\mathrm{dm} \\ \mathrm{Height}=10\mathrm{dm} \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\times (\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{length}\times \mathrm{height}) \\ =2\times (6\times 8+8\times 10+6\times 10) \\ =2\times (48+80+60) \\ =376{\mathrm{dm}}^2 \\ \left(\mathrm{iii}\right) \\ \mathrm{Dimensions}\mathrm{of}\mathrm{the}\mathrm{cuboid}: \\ \mathrm{Length}=2\mathrm{m} \\ \mathrm{Breadth}=4\mathrm{m} \\ \mathrm{Height}=5\mathrm{m} \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\times (\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{length}\times \mathrm{height}) \\ =2\times (2\times 4+4\times 5+2\times 5) \\ =2\times (8+20+10) \\ =76{\mathrm{m}}^2 \\ \left(\mathrm{iv}\right) \\ \mathrm{Dimensions}\mathrm{of}\mathrm{the}\mathrm{cuboid}: \\ \mathrm{Length}=3.2\mathrm{m} \\ =3.2\times 10\mathrm{dm}(1\mathrm{m}=10\mathrm{dm}) \\ =32\mathrm{dm} \\ \mathrm{Breadth}=30\mathrm{dm} \\ \mathrm{Height}=250\mathrm{cm} \\ =250\times \frac{1}{10}\mathrm{dm}(10\mathrm{cm}=1\mathrm{dm}) \\ =25\mathrm{dm} \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\times (\mathrm{length}\times \mathrm{breadth}+\mathrm{breadth}\times \mathrm{height}+\mathrm{length}\times \mathrm{height}) \\ =2\times (32\times 30+30\times 25+32\times 25) \\ =2\times (960+750+800) \\ =5020{\mathrm{dm}}^2 \end{gathered}$$