Find the surface area of a cuboid whose
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.

Solution:

(i) Dimension of the cuboid :

Length $=10 \mathrm{~cm}$

Breadth $=12 \mathrm{~cm}$

Height $=14 \mathrm{~cm}$

Surface area of the cuboid $=2 \times($ length $\times$ breadth $+$ breadth $\times$ height $+$ length $\times$ height $)$

$=2 \times(10 \times 12+12 \times 14+10 \times 14)$

$=2 \times(120+168+140)$

$=856 \mathrm{~cm}^{2}$

(ii) Dimensions of the cuboid :

Length $=6 \mathrm{dm}$

Breadth $=8 \mathrm{dm}$

Height $=10 \mathrm{dm}$

Surface area of the cuboid $=2 \times($ length $\times$ breadth $+$ breadth $\times$ height $+$ length $\times$ height $)$

$=2 \times(6 \times 8+8 \times 10+6 \times 10)$

$=2 \times(48+80+60)$

$=376 \mathrm{dm}^{2}$

(iii) Dimensions of the cuboid :

Length $=2 \mathrm{~m}$

Breadth $=4 \mathrm{~m}$

Height $=5 \mathrm{~m}$

Surface area of the cuboid $=2 \times($ length $\times$ breadth $+$ breadth $\times$ height $+$ length $\times$ height $)$

$=2 \times(2 \times 4+4 \times 5+2 \times 5)$

$=2 \times(8+20+10)$

$=76 \mathrm{~m}^{2}$

(iv) Dimensions of the cuboid:

Length $=3.2 \mathrm{~m}$

$=3.2 \times 10 \mathrm{dm} \quad(1 \mathrm{~m}=10 \mathrm{dm})$

$=32 \mathrm{dm}$

Breadth $=30 \mathrm{dm}$

Height $=250 \mathrm{~cm}$

$=250 \times \frac{1}{10} \mathrm{dm} \quad(10 \mathrm{~cm}=1 \mathrm{dm})$

$=25 \mathrm{dm}$

Surface area of the cuboid $=2 \times($ length $\times$ breadth $+$ breadth $\times$ height $+$ length $\times$ height $)$

$=2 \times(32 \times 30+30 \times 25+32 \times 25)$

$=2 \times(960+750+800)$

$=5020 \mathrm{dm}^{2}$