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Question

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 =(Length×Breadth×Height) cubic units
Total surface area =2(lb+bh+lh) sq units
Lateral surface area =2l+b×h sq units

(i) Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume =(Length×Breadth×Height) = (22×12×7.5)=1980 cm3
Total surface area =2(lb+bh+lh)= 222×12+22×7.5+12×7.5=2264+165+90=1038 cm2
Lateral surface area =2l+b×h=222+12×7.5=510 cm2

(ii) Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume =(Length×Breadth×Height) = (15×6×0.9)=81 m3
Total surface area=2(lb+bh+lh) = 215×6+15×0.9+6×0.9=290+13.5+5.4=217.8 m2
Lateral surface area =2l+b×h=215+6×0.9=37.8 m2

(iii) Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume =(Length×Breadth×Height) = (24×0.25×6)=36 m3
Total surface area=2(lb+bh+lh) = 224×0.25+24×6+0.25×6=26+144+1.5=303 m2
Lateral surface area =2l+b×h=224+0.25×6=291 m2

(iv) Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume =(Length×Breadth×Height) = (0.48×0.6×1)=0.288 m3
Total surface area =2(lb+bh+lh)= 20.48×0.6+0.48×1+0.6×1=20.288+0.48+0.6=2.736 m2
Lateral surface area =2l+b×h=20.48+0.6×1=2.16 m2

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