Worksheets · Geometry

Scale factor, area and volume worksheet

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 preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Scale Factor, Area and Volume

Date Period

Answer each question.

  1. Find how the area changes

    Every side of a rectangle is doubled. Its area is multiplied by what?
  2. The side of a square is tripled. Its area is multiplied by what?
  3. The side of a square is quadrupled. Its area is multiplied by what?
  4. Every side of a triangle is halved. Its area is multiplied by what?
  5. Every side of a triangle is divided by 3. Its area is multiplied by what?
  6. The radius of a circle is quadrupled. Its area is multiplied by what?
  7. Every side of a triangle is doubled. Its area is multiplied by what?

  1. Find how the volume changes

    The radius and height of a cone are divided by 3. Its volume is multiplied by what?
  2. The edge of a cube is halved. Its volume is multiplied by what?
  3. Every edge of a square pyramid is tripled. Its volume is multiplied by what?
  4. Every edge of a square pyramid is multiplied by 5. Its volume is multiplied by what?
  5. Every edge of a square pyramid is doubled. Its volume is multiplied by what?
  6. The edge of a cube is quadrupled. Its volume is multiplied by what?
  7. The radius and height of a cone are multiplied by 5. Its volume is multiplied by what?

  1. Use length, area and volume ratios of similar solids

    The volumes of two similar statues are in the ratio 729:1000. What is the ratio of their surface areas, smaller to larger?
  2. For two similar cones, the ratio of the surface areas is 49:81. Write the ratio of the matching lengths, smaller to larger.
  3. Two similar pyramids have heights of 9 cm and 11 cm. The smaller one has a surface area of 81 square cm. Find the surface area of the larger one.
  4. The two boxes are similar, and the numbers are the lengths of matching edges. Find the ratio of their volumes, smaller to larger.79
  5. Two similar statues have heights of 7 cm and 9 cm. The larger one has a volume of 2187 cubic cm. Find the volume of the smaller one.
  6. The two boxes are similar, and the numbers are the lengths of matching edges. Find the ratio of their surface areas, smaller to larger.89

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Scale Factor, Area and VolumeAnswer keyVersion 1

Date Period

Answer each question.

  1. Find how the area changes

    Every side of a rectangle is doubled. Its area is multiplied by what?4
  2. The side of a square is tripled. Its area is multiplied by what?9
  3. The side of a square is quadrupled. Its area is multiplied by what?16
  4. Every side of a triangle is halved. Its area is multiplied by what?14
  5. Every side of a triangle is divided by 3. Its area is multiplied by what?19
  6. The radius of a circle is quadrupled. Its area is multiplied by what?16
  7. Every side of a triangle is doubled. Its area is multiplied by what?4

  1. Find how the volume changes

    The radius and height of a cone are divided by 3. Its volume is multiplied by what?127
  2. The edge of a cube is halved. Its volume is multiplied by what?18
  3. Every edge of a square pyramid is tripled. Its volume is multiplied by what?27
  4. Every edge of a square pyramid is multiplied by 5. Its volume is multiplied by what?125
  5. Every edge of a square pyramid is doubled. Its volume is multiplied by what?8
  6. The edge of a cube is quadrupled. Its volume is multiplied by what?64
  7. The radius and height of a cone are multiplied by 5. Its volume is multiplied by what?125

  1. Use length, area and volume ratios of similar solids

    The volumes of two similar statues are in the ratio 729:1000. What is the ratio of their surface areas, smaller to larger?81:100
  2. For two similar cones, the ratio of the surface areas is 49:81. Write the ratio of the matching lengths, smaller to larger.7:9
  3. Two similar pyramids have heights of 9 cm and 11 cm. The smaller one has a surface area of 81 square cm. Find the surface area of the larger one.121 square cm
  4. The two boxes are similar, and the numbers are the lengths of matching edges. Find the ratio of their volumes, smaller to larger.79343:729
  5. Two similar statues have heights of 7 cm and 9 cm. The larger one has a volume of 2187 cubic cm. Find the volume of the smaller one.1029 cubic cm
  6. The two boxes are similar, and the numbers are the lengths of matching edges. Find the ratio of their surface areas, smaller to larger.8964:81

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

The edge of a cube is doubled. Its volume is multiplied by what?

  1. Volume uses three lengths.
  2. So the factor is 2 cubed.
  3. 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? → 14
What happens to the surface area
The radius and height of a cone are halved. Its surface area is multiplied by what? → 14
What happens to the volume
The radius and height of a cone are halved. Its volume is multiplied by what? → 18
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 are halved. Find the new volume. → 7
Areas and volumes of similar figures
The volumes of two similar cones are in the ratio 1:27. What is the ratio of their surface areas, smaller to larger? → 1:9
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
Scale factor, area and volume ratios from the dimensions
Two similar boxes: one is 10 by 4 by 8, the other is 20 by 8 by 16. Give the scale factor, the ratio of surface areas and the ratio of volumes, small to large. → 1:2, 1:4, 1:8

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 8: 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, areas and volumes of similar figures, scale factor from areas or volumes, then the other measure and scale factor, area and volume ratios from the dimensions. 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.