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Geometry and measurementGrades 7–8

Surface area of cylinders worksheets

Draws cylinders with the radius and height labeled and asks for surface area, volume or both. Answers are rounded to tenths using 3.14 or left in terms of π. Choose 2 to 12 problems with an answer key.

By Paul Gunder. Free to print for home, classroom and office use; see how our printables are made.

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Surface Area of Cylinders2 pages, answer key from page 2 · US Letter

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NameDateScoreSurface Area of CylindersVolume = π r² h. Surface area = 2π r² + 2π r h. For cylinders use π ≈ 3.14 and round to the nearest tenth. Writecubic units for volume and square units for area.1.r = 3 cmh = 12 cmSurface area = ____________2.r = 10 inh = 3 inSurface area = ____________3.r = 9 cmh = 3 cmSurface area = ____________4.r = 4 fth = 10 ftSurface area = ____________5.r = 5 mh = 3 mSurface area = ____________6.r = 11 inh = 10 inSurface area = ____________PrintablePal.com · free printablesSurface Area of Cylinders
Worksheet, page 1
Surface Area of Cylinders: answer key1.r = 3 cmh = 12 cmSurface area = ____________SA = 282.6 cm²2.r = 10 inh = 3 inSurface area = ____________SA = 816.4 in²3.r = 9 cmh = 3 cmSurface area = ____________SA = 678.2 cm²4.r = 4 fth = 10 ftSurface area = ____________SA = 351.7 ft²5.r = 5 mh = 3 mSurface area = ____________SA = 251.2 m²6.r = 11 inh = 10 inSurface area = ____________SA = 1450.7 in²PrintablePal.com · free printablesAnswer key
Answer key, page 1

On this page

A can, taken apart

Peel the label off a soup can and it lies flat as a rectangle. The lid and the bottom are two circles. That is the whole idea behind the surface area of a cylinder: two circles plus one rectangle. The rectangle's width is the distance around the circle, 2πr, and its height is the cylinder's height. This is why the formula has two terms.

The page is aimed at grades 7 and 8. It assumes students know the area of a circle and can handle a formula with π. For students who need the flat-faced version first, the surface area and volume page uses prisms and cubes.

What is printed

Each cylinder is drawn with a dashed hidden edge at the base. The radius is marked with a short line from the center of the top circle to its edge, labeled r, and the height is labeled h on the right side. Both values run from 2 to 12 with units of centimeters, meters, inches or feet. The instruction line shows the formulas: volume = π r² h and surface area = 2π r² + 2π r h. Two drawings fit across a row.

Notice that the radius is given, not the diameter. That removes one halving step so the page can focus on the formula.

Choosing the settings

  • Solids. Set to "Cylinders" on this page. Mixing in prisms and cubes is possible if you want a review sheet.
  • Find. The preset asks for surface area only. "Volume" or "Volume and surface area" gives a full review of cylinder formulas.
  • Cylinder answers. "Use 3.14 and round to tenths" is for calculator practice. "Leave in terms of π" gives answers such as 130π, which is the cleaner choice when students are learning the formula, since there is no decimal arithmetic to slip on.
  • Number of problems. Six fits a page with room for working.

Worked example: r = 5 cm, h = 8 cm

  1. Area of one circle. π r² = π × 5² = 25π. There are two ends, so the ends together are 2 × 25π = 50π.
  2. Side (the unrolled label). 2π r h = 2 × π × 5 × 8 = 80π.
  3. Add. 50π + 80π = 130π cm².
  4. With 3.14. 130 × 3.14 = 408.2, so the surface area is about 408.2 cm².

For the same can, volume is π r² h = π × 25 × 8 = 200π, which is 628 cm³ with 3.14.

Another quick one: r = 7 and h = 3. The ends are 2 × 49π = 98π, the side is 2 × 7 × 3 = 42π, and the total is 140π. With 3.14, that is 439.6.

What to check on the key

  • One circle, not two. The answer will be missing a whole πr² term. Remind students that a can has a lid and a bottom.
  • Forgetting the side. The answer is only 50π, the ends alone.
  • Squaring the wrong thing. Writing (2r)² or 2πr² for the side.
  • Rounding too early. The key finds the exact multiple of 3.14 first and rounds once at the end. A student who rounds along the way may be off by a tenth.
  • Wrong units. Surface area is in square units, volume is in cubic units.

Teaching tip

Let students cut out a paper cylinder and roll a rectangle into a tube. Measure the rectangle's width and compare it with the circumference of a circle that fits the end. Then the formula 2πrh stops being a string of symbols and turns into something visible.

Sources

  1. Common Core State Standards: Grade 7 Geometry (7.G.B.6, surface area of three-dimensional objects composed of polygons and other shapes) thecorestandards.org
  2. Common Core State Standards: Grade 8 Geometry (8.G.C.9, volume of cylinders) thecorestandards.org