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Volume of a Cuboid and Cube


Volume of a cube = (side)3 = (edge)3 cubic units

Longest diagonal of a cube = a units

 

Example

Find the volume of a cube in each of the following:
(i) 9cm (ii) 3cm

 

Solution

Let the edge of the cube = a cm

Volume of the cube = a3 cu. cm.

(i) a = 9 cm

Hence volume = a3 = 93 = 729 cu. cm

(ii) a = 3 cm

Hence volume = a3 = 33 = 27 cu. cm


 


Volume of a Cuboid


Volume of a cuboid = length ´ breadth ´ height = lbh cubic units

Longest diagonal of a cuboid = 

 

Example

Find the volume of a cuboid in each of the following:

(i) length = 8 cm, breadth = 5 cm, and height = 4 cm

(ii) length = 12 cm, breadth = 8.5 cm, height = 5 cm

 

Solution

(i) Volume of a cuboid = length ´ breadth ´ height 
                               = 8
´ 5 ´ 4 = 160 cm3

(iii) Volume of a cuboid= l
´ b ´ h = 12 ´ 8.5 ´ 5 = 510 cm3
 


 

Example

Find the longest pole length that can be put in a room of 10 m ´ 10 m ´ 5 m dimensions.
 

Solution

Longest pole will be equal to the longest diagonal of the room

     = 

     =

     = 15 m

 

 





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