Dimensional change questions II: Answer key below.

If you've found you are not solid yet with these problems,

slow down and start with Dimensional change questions I.

1a. There is a regular cylinder, which has a height equal to its radius. If the radius and height are both increased by 20%, by what % does the total volume of the cylinder increase?

1b. If the radius and height are both decreased by 20%, by what % does the total volume of the cylinder decrease?

1c. If the radius is increased by 50% and the height is decreased by 25%, what % of the volume of the original cylinder does the volume of the new cylinder represent?

1d. If the radius is increased by 25% and the height is decreased by 50%, what % of the volume of the original cylinder does the volume of the new cylinder represent?

1e. If the height is increased by 300%, what % does the radius need to be decreased by for the volume to remain the same?

2. If the side of a cube is increased by 30%, by what % does the total surface area of the cube increase? By what % does the volume increase?

3a. If the volume of a cube increases by 174.4%, by what % does the total surface area of the cube increase?

3b. By what % did the side length of the cube increase?

Answer key to dimensional change questions II:

1a. There is a regular cylinder, which has a height equal to
its radius. If the radius and height are both increased by 20%, by what % does
the total volume of the cylinder increase?

**72.8%**

1b. If the radius and height are both decreased by 20%, by
what % does the total volume of the cylinder decrease?

**48.8% (Only 0.8**

^{3}= 0.512 = 51.2% of the original percentage left and 100% - 51.2% = 48.8%.)
1c. If the radius is increased by 50% and the height is
decreased by 25%, what % of the volume of the original cylinder does the volume
of the new cylinder represent?

**168.75%**

1d. If the radius is increased by 25% and the height is
decreased by 50%, what % of the volume of the original cylinder does the volume
of the new cylinder represent?

**78.125%**

1e. If the height is increased by 300%, what % does the
radius need to be decreased by for the volume to remain the same?

**50%**

2. If the side of a cube is increased by 30%, by what % does
the total surface area of the cube increase? By what % does the volume
increase?

**The surface area will increase 69% and the volume will increase 119.7%**

3a. If the volume of a cube increases by 174.4%, by what % does
the total surface area of the cube increase?

**96%**

3b. By what % did the side length of the cube increase?

**40%**