Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm
(ii) length = 15 m, breadth = 6 m and height = 9 dm
(iii) length = 24 m, breadth = 25 cm and height = 6 m
(iv) length = 48 cm, breadth = 6 dm and height = 1 m

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Solution

Volume of a cuboid $= (L e n g t h \times B r e a d t h \times H e i g h t)$ cubic units
Total surface area $= 2 (l b + b h + l h)$ sq units
Lateral surface area $= [2 (l + b) \times h]$ sq units

(i) Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume $= (L e n g t h \times B r e a d t h \times H e i g h t)$ = $(22 \times 12 \times 7.5) = 1980 c m^{3}$
Total surface area $= 2 (l b + b h + l h)$ $= 2 [(22 \times 12) + (22 \times 7.5) + (12 \times 7.5)] = 2 [264 + 165 + 90] = 1038 c m^{2}$
Lateral surface area $= [2 (l + b) \times h]$ $= 2 (22 + 12) \times 7.5 = 510 c m^{2}$

(ii) Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume $= (L e n g t h \times B r e a d t h \times H e i g h t)$ = $(15 \times 6 \times 0.9) = 81 m^{3}$
Total surface area $= 2 (l b + b h + l h)$ $= 2 [(15 \times 6) + (15 \times 0.9) + (6 \times 0.9)] = 2 [90 + 13.5 + 5.4] = 217.8 m^{2}$
Lateral surface area $= [2 (l + b) \times h]$ $= 2 (15 + 6) \times 0.9 = 37.8 m^{2}$

(iii) Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume $= (L e n g t h \times B r e a d t h \times H e i g h t)$ = $(24 \times 0.25 \times 6) = 36 m^{3}$
Total surface area $= 2 (l b + b h + l h)$ $= 2 [(24 \times 0.25) + (24 \times 6) + (0.25 \times 6)] = 2 [6 + 144 + 1.5] = 303 m^{2}$
Lateral surface area $= [2 (l + b) \times h]$ $= 2 (24 + 0.25) \times 6 = 291 m^{2}$

(iv) Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume $= (L e n g t h \times B r e a d t h \times H e i g h t)$ = $(0.48 \times 0.6 \times 1) = 0.288 m^{3}$
Total surface area $= 2 (l b + b h + l h)$ $= 2 [(0.48 \times 0.6) + (0.48 \times 1) + (0.6 \times 1)] = 2 [0.288 + 0.48 + 0.6] = 2.736 m^{2}$
Lateral surface area $= [2 (l + b) \times h]$ $= 2 (0.48 + 0.6) \times 1 = 2.16 m^{2}$

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