Math Practice Problems - Area And Volume Proportions

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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=8, Mode=volume

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

Complexity=8

Find the area, volume, or increase factor of the following shapes after the transformations have been made.

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 circle has an area of 24. If the radius is increased by a factor of 3, what is the new area of the circle?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 24 × (3) ² since circle areas = πr² which is dependent on a square term New Area = 216

#	Problem	Correct Answer	Your Answer
2	A square has an area of 29. 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 = 29 × (2) ² since square area = s² which is dependent on a square term New Area = 116

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 18. If the radius is increased by a factor of 4, what is the new volume of the sphere?	New Volume =
Solution New volume = Original volume × (Increase factor)^{(Number of dimensions increased)} New volume = 18 × (4)³ since sphere volume = (4/3)πr³ and the radius was what was changed. New volume = 1152

#	Problem	Correct Answer	Your Answer
2	A sphere has a volume of 30. If the radius is increased by a factor of 4, what is the new volume of the sphere?	New Volume =
Solution New volume = Original volume × (Increase factor)^{(Number of dimensions increased)} New volume = 30 × (4)³ since sphere volume = (4/3)πr³ and the radius was what was changed. New volume = 1920

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 rectangle has an area of 15. If the base is increased by a factor of 3, what is the new area of the rectangle?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 15 × (3) ¹ since rectangle area = bh and we are changing the base length New Area = 45

#	Problem	Correct Answer	Your Answer
2	A triangle has an area of 8. If the height is increased by a factor of 3, what is the new area of the triangle?	New Area =
Solution New area = Original area × (Increase factor) ^{(Number of dimensions increased)} New area = 8 × (3) ¹ since triangle area = bh/2 and we are changing the height length New Area = 24

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