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 0.83 = 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%
