Two similar solids scale 2:3. The smaller has volume 16
Volumes scale by the cube.
Two cubed is 8, three cubed is 27.
Sixteen times 27 over 8.
The answer is 54.
Where students go wrong
Using the plain scale factor on an area or a volume. Only lengths scale by k; an area needs k squared and a volume k cubed, and using k everywhere gives an answer far too small.
Also called scale factor area volume, similar figures area ratio or cube of the scale factor.
What you can put on this worksheet
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 solids 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 solids 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 2: 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.
Using the plain scale factor on an area or a volume. Only lengths scale by k; an area needs k squared and a volume k cubed, and using k everywhere gives an answer far too small.