Worksheets · Geometry

Volume and surface area worksheet for Geometry

Prisms and cylinders are base area times height. Pyramids and cones are a third of that. Surface area adds up the faces: the two bases plus the sides for prisms and cylinders, the base plus the slanted sides for a cone. Spheres have their own two formulas and everything stays in terms of pi.

Also taught in Pre-Algebra, at its own level and with its own examples.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Volume and Surface Area

Date Period

Answer each question. Leave answers in terms of π unless the question asks you to round.

  1. Find the volume of a cylinder

    Find the volume of the cylinder.r = 2h = 7
  2. Find the volume. Leave π in your answer.r = 5h = 10

  1. Find the surface area of a cylinder

    The base of a cylinder has circumference 16π, and the cylinder is 12 units tall. Find its total surface area.
  2. An open-topped cylindrical tank has radius 3 and height 4. Find the area of its sides and bottom.

  1. Find a rectangular prism's height from its volume

    The volume is 385. Find the height.7h5
  2. The volume is 608. Find the height.2h19

  1. Find the surface area of a rectangular prism

    Find the surface area.528
  2. Find the surface area.584

  1. Find the volume of a cone

    Find the volume of the cone.d = 9h = 5
  2. Find the exact volume of the cone.r = 7.5h = 7

  1. Find a length from a cone's surface area

    The cone's total surface area is 216π. Find its height h.r = 9h
  2. The total surface area is 4050π. Find the slant height.r = 27ℓ

  1. Find the volume of a square pyramid

    The base is a square. Find the volume.3h = 2
  2. The base is a square. Find the volume.4h = 4

  1. Find the volume of a sphere

    Find the exact volume of the sphere.d = 15
  2. Find the volume.d = 13

  1. Find the surface area of a sphere

    A great circle of a sphere has circumference 90π. Find the surface area of the sphere.

  1. Find the volume of a composite solid

    A cone is carved out of a cylinder. They share the base, radius 5, and the height, 8. Find the volume that is left. Leave π in the answer.

  1. Find mass from density

    An iron bar is a box 2 cm by 4 cm by 20 cm. The density of iron is 7.9 g/cm3. Find its mass.

  1. Name and measure solids of revolution

    A semicircle of radius 1 is rotated about its diameter. Name the solid and find its volume.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Volume and Surface AreaAnswer keyVersion 1

Date Period

Answer each question. Leave answers in terms of π unless the question asks you to round.

  1. Find the volume of a cylinder

    Find the volume of the cylinder.r = 2h = 728π
  2. Find the volume. Leave π in your answer.r = 5h = 10250π

  1. Find the surface area of a cylinder

    The base of a cylinder has circumference 16π, and the cylinder is 12 units tall. Find its total surface area.320π
  2. An open-topped cylindrical tank has radius 3 and height 4. Find the area of its sides and bottom.33π

  1. Find a rectangular prism's height from its volume

    The volume is 385. Find the height.7h511
  2. The volume is 608. Find the height.2h1916

  1. Find the surface area of a rectangular prism

    Find the surface area.528132
  2. Find the surface area.584184

  1. Find the volume of a cone

    Find the volume of the cone.d = 9h = 51354π
  2. Find the exact volume of the cone.r = 7.5h = 75254π

  1. Find a length from a cone's surface area

    The cone's total surface area is 216π. Find its height h.r = 9h12
  2. The total surface area is 4050π. Find the slant height.r = 27ℓ123

  1. Find the volume of a square pyramid

    The base is a square. Find the volume.3h = 26
  2. The base is a square. Find the volume.4h = 4643

  1. Find the volume of a sphere

    Find the exact volume of the sphere.d = 1511252π
  2. Find the volume.d = 1321976π

  1. Find the surface area of a sphere

    A great circle of a sphere has circumference 90π. Find the surface area of the sphere.8100π

  1. Find the volume of a composite solid

    A cone is carved out of a cylinder. They share the base, radius 5, and the height, 8. Find the volume that is left. Leave π in the answer.4003π

  1. Find mass from density

    An iron bar is a box 2 cm by 4 cm by 20 cm. The density of iron is 7.9 g/cm3. Find its mass.1264 g

  1. Name and measure solids of revolution

    A semicircle of radius 1 is rotated about its diameter. Name the solid and find its volume.Sphere, 43π

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

How to do these

Find the volume of a cone with radius 3 and height 4

  1. The matching cylinder would be 9 pi times 4.
  2. A cone is a third of it.

The answer is 12π.

Where students go wrong

Using the slant height where the vertical height belongs. Volume needs the perpendicular height; surface area is the one that wants the slant. On these sheets the two are never the same number.

Also called volume and surface area of solids or 3D figures review.

What you can put on this worksheet

Volume of a cylinder
Work out the volume of the cylinder. — a cylinder with radius 7 and height 6 → 294π
Surface area of a cylinder
Find the total surface area of a cylinder with radius 7 and height 6. → 182π
Volume of a prism
Find the volume. — a rectangular prism 7 by 8 by 6 → 336
Surface area of a prism
Find the surface area. — a rectangular prism 7 by 8 by 6 → 292
Volume of a cone
A cone has radius 16 and height 30. Find its volume. → 2560π
Surface area of a cone
Find the exact surface area of the cone. — a cone with radius 16 and slant height 34 → 800π
Volume of a pyramid
The base is a square. Find the volume. — a square pyramid with base edge 8 and height 9 → 192
Volume of a sphere
Find the volume of the sphere. — a sphere with radius 15 → 4500π
Surface area of a sphere
Find the surface area of the sphere. — a sphere with radius 15 → 900π
The radius from the surface area
The surface area is 900π. Find r. — a sphere with radius r, labeled r → 15
Decimal sizes, rounded to the tenth
Find the volume of the rectangular prism to the nearest tenth. — a rectangular prism 7.6 by 1.7 by 5.3 → 68.5
Composite solids
A silo is a cylinder of radius 5 and height 12 topped by a hemisphere of the same radius. Find its volume. Leave π in the answer. → 11503π
Mass and density
A lead bar is a box 4 cm by 2 cm by 12 cm. The density of lead is 11.3 g/cm3. Find its mass. → 1084.8 g
Solids of revolution
A 6 by 7 rectangle is rotated about its side of length 7. Name the solid and find its volume. → Cylinder, 252π

Questions about these worksheets

Yes. Every volume and surface area 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 volume and surface area 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 14: volume of a cylinder, surface area of a cylinder, volume of a prism, surface area of a prism, volume of a cone, surface area of a cone, volume of a pyramid, volume of a sphere, surface area of a sphere, the radius from the surface area, decimal sizes, rounded to the tenth, composite solids, mass and density and solids of revolution. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the slant height where the vertical height belongs. Volume needs the perpendicular height; surface area is the one that wants the slant. On these sheets the two are never the same number.