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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=5, Mode=area

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

 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 = 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 =

### Complexity=8, Mode=volume

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

 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 = 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 =

### Complexity=8

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

 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 = 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 =

### Complexity=5, Mode=area

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

1A 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
2A 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.

1A 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
2A 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.

1A 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