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These sample problems below for Area And Volume Proportions were generated by the MathScore.com engine.

## Sample Problems For Area And Volume Proportions

### Complexity=5, Mode=area

Find the area of the following shapes after the transformations have been made.
 1 A triangle has an area of 9. If the height is increased by a factor of 4, what is the new area of the triangle? New Area = 2 A square has an area of 10. If the side length is increased by a factor of 3, what is the new area of the square? New Area =

### Complexity=8, Mode=volume

Find the volume of the following shapes after the transformations have been made.
 1 A triangular prism has a volume of 17. If the base height is increased by a factor of 5, what is the new volume of the triangular prism? New Volume = 2 A cube has a volume of 20. If the side length is increased by a factor of 4, what is the new volume of the cube? New Volume =

### Complexity=8

Find the area, volume, or increase factor of the following shapes after the transformations have been made.
 1 A rectangular prism has a volume of 28. If the volume is changed to 56, by what factor was the base width increased? Increase Factor = 2 A cylinder has a volume of 24. If the base radius is increased by a factor of 4, what is the new volume of the cylinder? New Volume =

### Complexity=5, Mode=area

Find the area of the following shapes after the transformations have been made.
1A triangle has an area of 9. If the height is increased by a factor of 4, what is the new area of the triangle?
New Area =
Solution
New area = Original area × (Increase factor) (Number of dimensions increased)
New area = 9 × (4) 1 since triangle area = bh/2 and we are changing the height length
New Area = 36
2A square has an area of 10. If the side length is increased by a factor of 3, what is the new area of the square?
New Area =
Solution
New area = Original area × (Increase factor) (Number of dimensions increased)
New area = 10 × (3) 2 since square area = s2 which is dependent on a square term
New Area = 90

### Complexity=8, Mode=volume

Find the volume of the following shapes after the transformations have been made.
1A triangular prism has a volume of 17. If the base height is increased by a factor of 5, what is the new volume of the triangular prism?
New Volume =
Solution
New volume = Original volume × (Increase factor)(Number of dimensions increased)
New volume = 17 × (5)1 since triangular prism volume = (bh b/2)h where hb = the base height which is what was changed.
New volume = 85
2A cube has a volume of 20. If the side length is increased by a factor of 4, what is the new volume of the cube?
New Volume =
Solution
New volume = Original volume × (Increase factor)(Number of dimensions increased)
New volume = 20 × (4)3 since cube volume = s3 and the side length is what was changed.

### Complexity=8

Find the area, volume, or increase factor of the following shapes after the transformations have been made.
1A rectangular prism has a volume of 28. If the volume is changed to 56, by what factor was the base width increased?
Increase Factor =
Solution
New volume = Original volume × (Increase factor)
56 = 28 × (Increase factor)1 since rectangular prism volume = lwh and the width is what was changed.
Increase factor = 2