Two similar solids have sides in the ratio 2:3. The volume of the smaller is 40. Find the larger
Volumes scale by the cube of the ratio.
8 to 27, so multiply by 27 over 8.
The answer is 135.
Where students go wrong
Scaling area or volume by the plain ratio. Doubling every length multiplies area by four and volume by eight, not two, which is why a scale model weighs so much less than it looks like it should.
Also called scale factor, similar figures, ratio of areas or ratio of volumes.
What you can put on this worksheet
Matching sides, from the diagram
The polygons are similar. Find the matching side→ 21
Matching sides, from a description
Two similar polygons have corresponding sides 6 and 18. If another side of the larger is 21, find the matching side→ 7
From the smaller solid to the larger
The volume of the smaller is 54. Find the larger→ 128
From the larger solid to the smaller
The volume of the larger is 128. Find the smaller→ 54
Questions about these worksheets
Yes. Every similar figures sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the similar figures questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 4: matching sides, from the diagram, matching sides, from a description, from the smaller solid to the larger and from the larger solid to the smaller. Tick as many as you want and set how many of each, or let it spread them evenly.
Scaling area or volume by the plain ratio. Doubling every length multiplies area by four and volume by eight, not two, which is why a scale model weighs so much less than it looks like it should.