Math Practice Problems - Area And Volume Proportions

Area And Volume Proportions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=5, Mode=area

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

1.	A rectangle has an area of 9. If the base is increased by a factor of 5, what is the new area of the rectangle? New Area =
2.	A square has an area of 6. If the side length is increased by a factor of 2, 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 sphere has a volume of 26. If the radius is increased by a factor of 5, what is the new volume of the sphere? New Volume =
2.	A cube has a volume of 30. If the side length is increased by a factor of 2, 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 16. If the volume is changed to 80, by what factor was the base width increased? Increase Factor =
2.	A rectangle has an area of 9. If the base is increased by a factor of 4, what is the new area of the rectangle? New Area =

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 rectangle has an area of 9. If the base is increased by a factor of 5, what is the new area of the rectangle?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 9 × (5) ¹ since rectangle area = bh and we are changing the base length New Area = 45

#	Problem	Correct Answer	Your Answer
2	A square has an area of 6. If the side length is increased by a factor of 2, what is the new area of the square?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 6 × (2) ² since square area = s² which is dependent on a square term New Area = 24

Complexity=8, Mode=volume

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

#	Problem	Correct Answer	Your Answer
1	A sphere has a volume of 26. If the radius is increased by a factor of 5, what is the new volume of the sphere?	New Volume =
Solution New volume = Original volume × (Increase factor)^{(Number of dimensions increased)} New volume = 26 × (5)³ since sphere volume = (4/3)πr³ and the radius was what was changed. New volume = 3250

#	Problem	Correct Answer	Your Answer
2	A cube has a volume of 30. If the side length is increased by a factor of 2, what is the new volume of the cube?	New Volume =
Solution New volume = Original volume × (Increase factor)^{(Number of dimensions increased)} New volume = 30 × (2)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 16. If the volume is changed to 80, by what factor was the base width increased?	Increase Factor =
Solution New volume = Original volume × (Increase factor)^{80 = 16 × (Increase factor)¹ since rectangular prism volume = lwh and the width is what was changed. Increase factor = 5}

#	Problem	Correct Answer	Your Answer
2	A rectangle has an area of 9. If the base is increased by a factor of 4, what is the new area of the rectangle?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 9 × (4) ¹ since rectangle area = bh and we are changing the base length New Area = 36

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