Two similar solids have a scale factor of 2:3. The volume of the smaller is 72. Find the volume of the larger.243
Two similar solids have surface areas 147and 300. The volume of the smaller is 1029. Find the volume of the larger.3000
Corresponding lengths of two similar solids are in the ratio 3:4. If the smaller solid has volume 2592, what is the volume of the larger?6144
The volume of a cone is 54. A similar cone has a height of 4 where the first has 3. What is its volume?128
A model and a real silo are similar, with lengths in the ratio 8:11. The model has surface area 1280. Find the surface area of the real one.2420
The volume of a cylinder is 2376. A similar cylinder has a height of 7 where the first has 6. What is its volume?3773
Two similar solids have a scale factor of 1:3. The surface area of the smaller is 4. Find the surface area of the larger.36
A cylinder with a radius of 8 has volume 10752. Find the volume of a similar cylinder whose radius is 9.15309
Corresponding lengths of two similar solids are in the ratio 3:4. If the smaller solid has surface area 468, what is the surface area of the larger?832
A cone with a height of 3 has surface area 81. Find the surface area of a similar cone whose height is 6.324
Scale down similar solids
The two boxes are similar. The surface area of the larger box is 768. Find the surface area of the smaller box.300
A triangular prism with a height of 5 has surface area 75. Find the surface area of a similar triangular prism whose height is 3.27
Two similar cylinders have radii 7and 10. The surface area of the larger is 1700. Find the surface area of the smaller.833
A model and a real statue are similar, with lengths in the ratio 5:8. The real one has volume 7680. Find the volume of the model.1875
Two similar square pyramids have base edges 3and 4. The surface area of the larger is 32. Find the surface area of the smaller.18
The larger of two similar solids has volume 2000. Their surface areas are 600 (the larger) and 294. What is the volume of the smaller?686
Corresponding lengths of two similar solids are in the ratio 5:7. If the larger solid has volume 3773, what is the volume of the smaller?1375
The surface area of a square pyramid is 27. A similar square pyramid has a base edge of 1 where the first has 3. What is its surface area?3
The boxes are similar, with matching edges as marked. The larger box has volume 23000. What is the volume of the smaller box?7889
A model and a real tank are similar, with lengths in the ratio 5:6. The real one has volume 3024. Find the volume of the model.1750
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 the wrong answer: too small going up, too large going down.
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
Two similar triangular prisms have heights 3and 4. The volume of the smaller is 54. Find the volume of the larger.→ 128
From the larger solid to the smaller
A cone with a height of 4 has surface area 80. Find the surface area of a similar cone whose height is 3.→ 45
Are two solids similar? Scale factor
Two cylinders: one has radius 6 and height 7, the other has radius 12 and height 14. Are they similar? If so, give the ratio of their dimensions, small : large.→ Similar, 1:2
Scale factor from areas or volumes, then the other measure
Two prisms are similar. Their surface areas are 343 and 175. Find the scale factor, first to second.→ 7:5
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 4: from the smaller solid to the larger, from the larger solid to the smaller, are two solids similar? scale factor and scale factor from areas or volumes, then the other measure. 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 the wrong answer: too small going up, too large going down.