Scale every length by a number and the area goes up by that number squared, the volume by it cubed. It catches people out because the answer feels too big: double the edges of a cube and the volume is eight times what it was, not two.
The edge of a cube is doubled. Its volume is multiplied by what?
Volume uses three lengths.
So the factor is 2 cubed.
2 cubed is 8.
The answer is 8.
Where students go wrong
Using the scale factor as it stands. Doubling the sides does not double the area or the volume: area is multiplied by four and volume by eight, because each of them is built from more than one length.
Also called areas and volumes of similar solids, effects of changing dimensions or scale factor.
What you can put on this worksheet
What happens to the area
Every side of a rectangle is halved. Its area is multiplied by what?→ 41
What happens to the surface area
The radius and height of a cone is halved. Its surface area is multiplied by what?→ 41
What happens to the volume
The radius and height of a cone is halved. Its volume is multiplied by what?→ 81
The new area, from the old one
A rectangle has area 28. Every side is halved. Find the new area→ 7
The new volume, from the old one
A cone has volume 56. The radius and height is halved. Find the new volume→ 7
Areas and volumes of similar figures
Find the ratio of their volumes→ 27:1
Questions about these worksheets
Yes. Every scale factor, area and volume 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 scale factor, area and volume 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 6: what happens to the area, what happens to the surface area, what happens to the volume, the new area, from the old one, the new volume, from the old one and areas and volumes of similar figures. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the scale factor as it stands. Doubling the sides does not double the area or the volume: area is multiplied by four and volume by eight, because each of them is built from more than one length.