Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height.Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides. Since volume involves 3 sides it is measured in cubic units. Volume of a cuboid = (length × breadth × height) cubic units.= (l × b × h) cubic units. (Since area = ℓ × b) Volume of a cuboid = area of one surface × height cubic units Let us look at the given cuboid. The length of the cuboid = 5 cm The breadth of the cuboid = 3 cm The height of cuboid (thickness) = 2 cm The number of 1 cm cubes in the given cuboid = 30 cubes = 5 × 3 × 2 We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm. Therefore, volume of a cuboid = length × breadth × height Solved examples on volume of a cuboid: 1. Find the volume of a cuboid of dimensions 14 cm × 12 cm × 8 cm. Solution: Volume of cuboid = length × breadth × height. Here, length = 14 cm, breadth = 12 cm and height = 8 cm.Volume of cuboid = 14 × 12 × 8 cubic cm.= 1344 cubic cm. Therefore, volume of cuboid = 1344 cubic cm. 2. Michael made a shoe box with length 8 cm, breadth 6 cm and height 6 cm. Find the volume of the box. Solution: Volume of the shoe box = Length × breadth × height. = 8 × 6 × 6 = 288 cu cm. 3. A fish tank is 40 cm long, 15 cm broad and 10 cm high. What is its volume in cu cm? Solution: The length of the fish tank = 40 cm The breadth of the fish tank = 15 cm The height of the fish tank = 10 cm Therefore, the volume of the fish tank = length × breadth × height. = 40 × 15 × 10 cu. cm = 6000 cu cm. 4. Find the volume of a cuboid of dimensions 14 cm × 50 mm × 10 cm. Solution: Here, length = 14 cm, [Given,
breadth = 50 mm; we need to convert breadth to same unit and then
solve. We know, 10 mm = 1 cm. Therefore, 50 mm = 50/10 cm = 5 cm]. Breadth = 5 cm, Height = 10 cm. Volume of cuboid = length × breadth × height. = 14 × 5 × 10 = 700 cubic cm.Therefore, volume of cuboid = 700 cubic cm. Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve. 5. Find the volume of a cuboid of dimensions 17 mm × 0.2 cm × 12 mm in cu. cm. Solution: Given, length = 17 mm. We know, 10 mm = 1 cm.= 17/10 cm. = 1.7 cm.Therefore, length = 1.7 cm. Similarly, height = 12 mm.We know, 10 mm = 1 cm.= 12/10 cm.= 1.2 cm.Therefore, height = 1.2 cm. Volume of cuboid = length × breadth × height.Length = 1.7 cm, breadth = 0.2 cm and height = 1.2 cm. = 1.7 × 0.2 × 1.2 cu. cm. = 0.408 cu. cm.Therefore, volume of cuboid = 0.408 cubic cm. 6. Find the number of cubical boxes of cubical side 3 cm which can be accommodated in carton of dimensions 15 cm × 9 cm × 12 cm. Solution: Volume of box = side × side × side. = 3 × 3 × 3 = 27 cu. cm.Volume of carton = length × breadth × height. = 15 × 9 × 12 = 1620 cu. cm.Number of boxes = Volume of carton/Volume of each box. = 1620/27 = 60 Therefore, number of cubical boxes = 60. 7. How many bricks each 25 cm long, 10 cm wide and 7.5 cm thick will be required for a wall 20 m long, 2 m high and 0.75 m thick? If bricks sell at $900 per thousand what will it cost to build the wall? Solution: Volume of the wall = 20 m × 2 m × 0.75 m = 20 × 100 cm × 2 × 100 cm × 0.75 × 100 cm Volume of brick = 25 cm × 10 cm × 7.5 cm Number of bricks = Volume of the wall/Volume of the brick = 20 × 100 × 2 × 100 × 0.75 × 100/25 × 10 × 7.5 = 16000 The number of bricks = 16000 The cost of 1 thousand bricks = $ 900 The cost of building the wall = $ 900 × 16 = $ 14400 Note: While calculating the volume of a cuboid all the dimensions should be changed into the same unit. Questions and Answers on Cuboid: 1. Find the volume of each of the cuboids. (i) Length = 5 cm, Breadth = 4 cm and Height = 3 cm (ii) Length = 15 m, Breadth = 10 m and Height = 2 m (iii) Length = 0.5 m, Breadth = 3 m and Height = 4 m (iv) Length = 3.2 cm, Breadth = 2 cm and Height = 8 cm (v) Length = 5 m, Breadth = 1.5 m and Height = 1.2 m Answers: 1. (i) 60 cu cm (ii) 300 cu m (iii) 6 cu m (iv) 51.2 cu cm (v) 9 cu m 2. Find the volume of these tanks. (i) Length = 16 cm, Breadth = 60 cm and Height = 20 cm (ii) Length = 6 m, Breadth = 3 m and Height = 5 m (iii) Length = 2 m, Breadth = 1.5 m and Height = 1.5 m (iv) Length = 80 cm, Breadth = 20 cm and Height = 40 cm (v) Length = 1.2 m, Breadth = 1.2 m and Height = 1 m Answers: 2. (i) 19200 cu cm (ii) 90 cu m (iii) 4.5 cu m (iv) 64,000 cu cm (v) 1.44 cu m
● Volume. Units of Volume Cube. Cuboid. Practice Test on Volume. Worksheet on Volume. 5th Grade Geometry 5th Grade Math Problems From Volume of a Cuboid to HOME PAGE
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