Math Practice Topic: Area And Volume Proportions

Description: This topic deals with understanding how changing certain sides changes area and volume.

Adaptive Learning Progression: Area only, then volume only, then mixed.

Sample Levels (out of 3)

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

1.
A circle has an area of 8. If the radius is increased by a factor of 5, what is the new area of the circle?
New Area =
2.
A square has an area of 15. If the side length is increased by a factor of 2, what is the new area of the square?
New Area =

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 22. If the base width is increased by a factor of 4, what is the new volume of the rectangular prism?
New Volume =
2.
A cylinder has a volume of 19. If the base radius is increased by a factor of 3, what is the new volume of the cylinder?
New Volume =

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

1.
A triangle has an area of 22. If the area is changed to 66, by what factor was the height increased?
Increase Factor =
2.
A triangular prism has a volume of 28. If the volume is changed to 140, by what factor was the base height increased?
Increase Factor =

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