Find the volume, the lateral surface are and the total surface area of the cuboid whose dimensions are:
Question:

Find the volume, the lateral surface are and the total surface area of the cuboid whose dimensions are:
(i) length = 12 cm, breadth = 8 cm and height = 4.5 cm
(ii) length = 26 m, breadth = 14 m and height = 6.5 m
(iii) length = 15 m, breadth = 6 m and height = 5 dm
(iv) length = 24 m, breadth = 25 cm and height = 6 m

Solution:

(i)
Here, l = 12 cm, b = 8 cm, h = 4.5 cm

Volume of the cuboid $=l \times b \times h$

$=(12 \times 8 \times 4.5) \mathrm{cm}^{3}$

$=432 \mathrm{~cm}^{3}$

Total Surface area = 2(lb + lh+ bh)

$=2(12 \times 8+12 \times 4.5+8 \times 4.5) \mathrm{cm}^{2}$

$=2(96+54+36) \mathrm{cm}^{2}$

$=2 \times 186 \mathrm{~cm}^{2}$

$=372 \mathrm{~cm}^{2}$

Lateral surface area $=2(l+b) \times h$

$=[2(12+8) \times 4.5] \mathrm{cm}^{2}$

$=[2(20) \times 4.5] \mathrm{cm}^{2}$

$=40 \times 4.5 \mathrm{~cm}^{2}$

$=180 \mathrm{~cm}^{2}$

(ii)
Here, = 26 m; b = 14 m; h =6.5 m

Volume of the cuboid $=l \times b \times h$

$=(26 \times 14 \times 6.5) \mathrm{m}^{3}$

$=2366 \mathrm{~m}^{3}$

Total surface area = 2(lb + lh+ bh)

$=2(26 \times 14+26 \times 6.5+6.5 \times 14) \mathrm{m}^{2}$

$=2(364+169+91) \mathrm{m}^{2}$

$=2 \times 624 \mathrm{~m}^{2}$

$=1248 \mathrm{~m}^{2}$

Lateral surface area $=2(l+b) \times h$

$=[2(26+14) \times 6.5] \mathrm{m}^{2}$

$=[2 \times 40 \times 6.5] \mathrm{m}^{2}$

$=520 \mathrm{~m}^{2}$

(iii)
Here, l = 15 m; b = 6 m; h = 5 dm = 0.5 m

Volume of the cuboid $=l \times b \times h$

$=(15 \times 6 \times 0.5) \mathrm{m}^{3}$

$=45 \mathrm{~m}^{3}$

Total surface area = 2(lb + lh+ bh

$=2(15 \times 6+15 \times 0.5+6 \times 0.5) \mathrm{m}^{2}$

$=2(90+7.5+3) \mathrm{m}^{2}$

$=2 \times 100.5 \mathrm{~m}^{2}$

$=201 \mathrm{~m}^{2}$

Lateral surface area $=2(l+b) \times h$

$=[2(15+6) \times 0.5] \mathrm{m}^{2}$

$=[2 \times 21 \times 0.5] \mathrm{m}^{2}$

$=21 \mathrm{~m}^{2}$

(iv)
Here, = 24 m; b = 25 cm = 0.25 m; h =6 m

Volume of the cuboid $=l \times b \times h$

$=(24 \times 0.25 \times 6) \mathrm{m}^{3}$

$=36 \mathrm{~m}^{3}$

Total Surface area = 2(lb + lh+ bh)

$=2(24 \times 0.25+24 \times 6+0.25 \times 6) \mathrm{m}^{2}$

$=2(6+144+1.5) \mathrm{m}^{2}$

$=2 \times 151.5 \mathrm{~m}^{2}$

$=303 \mathrm{~m}^{2}$

Lateral surface area $=2(l+b) \times h$

$=[2(24+0.25) \times 6] \mathrm{m}^{2}$

$=[2 \times 24.25 \times 6] \mathrm{m}^{2}$

$=291 \mathrm{~m}^{2}$