If the linear dimensions of a solid are multiplied by a scale factor k, the volume is multiplied by k3.

Question

true or false i need help here please and thank you 

Answer 1

An easy way: Volume of original = LWH

Volume of enlarged: = (kL)(kW)(kH) = k³(LWH)

 

Yes, volume is multiplied by cube of the upscaling factor k.

Answer 2

We can look at this in terms of a single cube. In this case, we will have a cube with dimensions of 1x1x1.

 

If we solve for volume using the formula for a cube, length*width*height, we get that the volume would be 1.

 

If we now take the scale factor of k, and make it k=2, we have a cube that is the dimensions 2x2x2. If we use the same formula as above, we see that we now have 2*2*2 which would give us a volume of 8. This would be k³.

 

 

We can also do this starting with the 2x2x2 cube. If we start with the volume of 8, and we now change the dimensions by a factor of k=4, we end up with an 8x8x8 cube. This gives us a volume of 512.

 

For this to be true, 512=8*k³. If we plug in our k factor, we get that 512=8*4³=8*64=512.