3D solids
Compare volumes and surface areas of solids. Then change their dimensions to explore scaling and shape.
Cuboid volume and surface area
1 comparison · No time limit · Explore after checking
Example
Example
Does the taller cuboid necessarily have more volume?
Review the comparison
The cuboids have the same positive width w. A has height 8; B has height 4.
A has depth 3 units. B is deeper than A, but its depth is not specified.
One possible pair, drawn with a shared scale. Only the stated relationships are fixed.
Volume of cuboid A
Volume of cuboid B
Choose an answer to try the example.
Why?
Explore the relationship
Save two valid cases with different comparisons.
In this drawing
Need a clue?
Save one position, then move the controls until A and B have a different relationship. Equal is a different relationship too.
Example positions
Change B’s depth relative to A. B stays deeper than A while A stays twice as tall.
Two different comparisons under the same givens establish “Cannot be determined.”
Go further Apply the idea
Further practice does not change your comparison score.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
Discard the unfinished round?
Your answers from this round will be discarded. You can choose your settings before starting a new round.
Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Scale length, area and volumeCompare volumes and surface areas of solids. Then change their dimensions to explore scaling and shape.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used