Area And Volume Proportions Sample Problems

Math Practice Online: MathScore.com

Math Practice Online > free > lessons > Ohio > 8th grade > Area And Volume Proportions

If your child needs math practice, click here.

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

Copyright Accurate Learning Systems Corporation 2008.
MathScore is a registered trademark.