if all the dimensions of a rectangular prism are doubled,does the volume double?explain

Question

18in. multiply by 22in. multiply by  34in. 13464 is the value.

Answer 1

Old volume is LWH.

 

New volume is (2L)(2W)(2H).  That's 8 times as much.

Answer 2

If you double all of the dimensions of a rectangular prism, you create a similar prism with a scale factor of 2.  The surface area of the similar prism will increase as the square of the scale factor (2² = 4) and the volume will increase as the cube of the scale factor (2³ = 8).

 

Here's why.  Let the dimensions of the original prism be a, b, and c.  Its volume is:

 

V = a*b*c

 

Now double all of the dimensions: 2a, 2b, 2c.  The new volume is:

 

Volume = 2a*2b*2c = 2*2*2*a*b*c = 2³*(a*b*c)

 

Since a*b*c is the volume of the original prism, the volume of the larger prism is 2³=8 times larger.