Area And Volume Proportions Sample Problems

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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 =

Answers

Complexity=5, Mode=area

Find the area of the following shapes after the transformations have been made.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
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.

#	Problem	Correct Answer	Your Answer
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 =
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 h_b = the base height which is what was changed. New volume = 85

#	Problem	Correct Answer	Your Answer
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 =
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.

#	Problem	Correct Answer	Your Answer
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 =
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}

#	Problem	Correct Answer	Your Answer
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 =
Solution New volume = Original volume × (Increase factor)^{(Number of dimensions increased)} New volume = 24 × (4)² since cylinder volume = πr²h which is dependent on a square term and the cylinder base circle's radius was what was changed. New volume = 384

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