Question

If the sum of all the edges of a cube is 36 cm, then what will be the volume of that
cube? and answer will be 729cm³ how?
​

Answer 1

Answer :

27 cm³

Note :

• Cube : A cube is a three-dimensional solid object bounded by six square faces with three meeting at each vertex .
• A cube has 6 faces , 12 edges and 8 vertices .
• If the length of each edge of a cube is a units , then
• Volume = a³ cubic units
• Lateral surface area = a² sq. units
• Total surface area = a² sq. units

Solution :

• Given : Sum of all edges = 36 cm
• To find : Volume of cube = ?

Let the length of each edge of the cube be x cm .

Also ,

We know that , s cube has 12 edges .

Thus ,

=> Sum of all edges = x + x + x +....12 times

=> Sum of all edges = 12x

=> 36 = 12x

=> x = 36/12

=> x = 3

Hence ,

The length of each edge of the cube is 3 cm , ie. a = 3 cm

Now ,

The volume of the cube will be given as ;

=> V = a³

=> V = 3³ cm³

=> V = 27 cm³

Hence ,

The volume of the cube is 27 cm³ .