If all the dimensions of a rectangular solid are increased by 2 times, what is the change in the volume of the shape?

Guest Dec 14, 2014

#2**+10 **

If the dimensions of a solid double That is they (the lengths) are 2 times greater

then the surface area will increase by a factor of 2^2=4 That is it will be 4 times greater

and

the volume will increase by a factor of 2^3 =8. That is it will be 8 times greater.

**This is a really handy thing to know **

Melody
Dec 14, 2014

#2**+10 **

Best Answer

If the dimensions of a solid double That is they (the lengths) are 2 times greater

then the surface area will increase by a factor of 2^2=4 That is it will be 4 times greater

and

the volume will increase by a factor of 2^3 =8. That is it will be 8 times greater.

**This is a really handy thing to know **

Melody
Dec 14, 2014

#3**+5 **

I am just thinking here.

If we increase something by a factor of 1 this is meaningless. To a mathematician it means multiply by 1 so it stays the same and is not increased at all.

If you told a lay person in the street to increase the size of something by a factor of 1 they could either mistakenly add one unit to it or erroneously double the size. They could easily think that if it was 4 units long before and increase it by a factor of 1 that it must now be 8 units (what it was before plus one more of what it was before 1+1more) . Of course this is really increasing by a factor of 2 (1*2) but I can see how it could be very confusing.

Melody
Dec 14, 2014