Question

The volume of a cube is0.125 cubic cm if the length of its edges is increased three times by how much ites volume will increase

Answer 1

Answer:

The volume of the cube will increase by 27 times the original volume.

Step-by-step-explanation:

We have given that,

Volume of a cube = 0.125 cu.cm.

The length of the edges of the cube is increased three times.

We have to find how much times the volume will increase.

Now, we know that,

Volume of cube = ( Edge )³

⇒ 0.125 = ( Edge )³

⇒ ∛( 0.125 ) = Edge

⇒ Edge = ∛( 0.5 * 0.5 * 0.5 )

⇒ Edge = 0.5 cm

∴ Length of edge = 0.5 cm

Now,

New length of edge = 3 * Original length of edge

⇒ New length of edge = 3 * 0.5

⇒ New length of edge = 1.5 cm

Now,

New volume of cube = ( New edge )³

⇒ New volume of cube = ( 1.5 )³

⇒ New volume of cube = 1.5 * 1.5 * 1.5

⇒ New volume of cube = 2.25 * 1.5

⇒ New volume of cube = 3.375 cu.cm

Now,

Increase in volume = New volume / Original volume

⇒ Increase in volume = 3.375 / 0.125

⇒ Increase in volume = ( 3.375 * 1000 ) / ( 0.125 * 1000 )

⇒ Increase in volume = 3375 / 125

⇒ Increase in volume = 135 / 5

⇒ Increase in volume = 27

∴ The volume of the cube will increase by 27 times the original volume.