Question

Find the total surface area of the cuboids of length, breadth and height as given below:

(i) 12 cm, 10 cm, 5 cm (ii) 5 cm, 3.5 cm, 1.4 cm

(iii) 2.5 cm, 2 m, 2.4 m (iv) 8 m, 5 m, 3.5 m

Answer 1

(i) Length of the cuboid, l = 12 cm
Breadth of the cuboid, b = 10 cm
Height of the cuboid, h = 5 cm
∴ Total surface area of the cuboid = 2(l × b + b × h + h × l)
= 2(12 × 10 + 10 × 5 + 5 × 12)
= 2(120 + 50 + 60)
= 2 × 230
= 460 cm²

(ii) Length of the cuboid, l = 5 cm
Breadth of the cuboid, b = 3.5 cm
Height of the cuboid, h = 1.4 cm
∴ Total surface area of the cuboid = 2(l × b + b × h + h × l)
= 2(5 × 3.5 + 3.5 × 1.4 + 1.4 × 5)
= 2(17.5 + 4.9 + 7.0)
= 2 × 29.4
= 58.8 cm²

(iii) Length of the cuboid, l = 2.5 cm = $\frac{2.5}{100}$ m = 0.025 m [∵ 100 cm = 1 m]
Breadth of the cuboid, b = 2 m
Height of the cuboid, h = 2.4 m
∴ Total surface area of the cuboid = 2(l × b + b × h + h × l)
= 2(0.025 × 2 + 2 × 2.4 + 2.4 × 0.025)
= 2(0.05 + 4.8 + 0.06)
= 2 × 4.91
= 9.82 m²

(iv) Length of the cuboid, l = 8 m
Breadth of the cuboid, b = 5 m
Height of the cuboid, h = 3.5 m
∴ Total surface area of the cuboid = 2(l × b + b × h + h × l)
= 2(8 × 5 + 5 × 3.5 + 3.5 × 8)
= 2(40 + 17.5 + 28)
= 2 × 85.5
= 171 m²