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
(i) We know that,
Volume of cuboid = Length × Breadth × Height
= (22 × 12 × 7.5)
= 1980 cm3
We also know that,
Total Surface Area of cuboid = 2 (lb + bh + hl)
= 2 (22 × 12) + (22 × 7.5) + (12 × 7.5)
= 2 (264 + 165 + 90)
= 1038 cm2
Now,
Lateral surface area of cuboid = [2 (l + b) × h]
= 2 (22 + 12) × 7.5
= 510 cm2
(ii) We know that,
Volume of cuboid = Length × Breadth × Height
= (15 × 6 × 0.9)
= 81 m3
We also know that,
Total Surface Area of cuboid = 2 (lb + bh + hl)
= 2 (15 × 6) + (15 × 0.9) + (6 × 0.9)
= 2 (90 + 13.5 + 5.4)
= 217.8 m2
Now,
Lateral surface area of cuboid = [2 (l + b) × h]
= 2 (15 + 6) × 0.9
= 37.8 m2
(iii) We know that,
Volume of cuboid = Length × Breadth × Height
= (24 × 0.25 × 6)
= 36 m3
We also know that,
Total Surface Area of cuboid = 2 (lb + bh + hl)
= 2 (24 × 0.25) + (24 × 6) + (0.25 × 6)
= 2 (6 + 144 + 1.5)
= 303 m2
Now,
Lateral surface area of cuboid = [2 (l + b) × h]
= 2 (24 + 0.25) × 6
= 291 m2
(iv) We know that,
Volume of cuboid = Length × Breadth × Height
= (0.48 × 0.6 × 1)
= 0.288 m3
We also know that,
Total Surface Area of cuboid = 2 (lb + bh + hl)
= 2 (0.48 × 0.6) + (0.48 × 1) + (0.6 × 1)
= 2 (0.288 + 0.48 + 0.6)
= 2.736 m2
Now,
Lateral surface area of cuboid = [2 (l + b) × h]
= 2 (0.48 + 0.6) × 1
= 2.16 m2