Geometry and measurement

Cylinder Nets and Surface Area

Unroll cylinders into rectangles and circles, find matching net dimensions, and calculate curved and total surface areas.

Grades 7–8 practice · 6 questions · Free to print · Answers included

Download free worksheetPDFDownload worked answersPDF

Make sense of the method

A closed right circular cylinder has two circular ends and one curved side. A net shows the side as a rectangle and the ends as circles.

The rectangle’s wrapping length is the circle circumference, 2πr; its other dimension is the cylinder height. Net sketches are schematic, so use labels rather than screen measurements.

  1. Identify the radius and perpendicular height.
  2. Label the rectangle with length 2πr and width h.
  3. Add one circle for each closed end that is present.
  4. Calculate and add only the requested component areas, using square units.

A worked example

A closed cylinder has radius 2 cm and height 6 cm. Give its net dimensions and total surface area in terms of π.

Example closed cylinder netA rectangle and 2 circular ends. Circle radius: 2 cm. Rectangle height: 6 cm. Rectangle length equals the circumference. Drawing not to scale.r = 2 cmLength = circumferenceHeight: 6 cm2 circular ends + one curved side · not to scale
Example closed cylinder net
  1. The wrapping length is 2π × 2 = 4π cm.
  2. Rectangle area = 4π × 6 = 24π cm².
  3. Two circular ends contribute 2 × π × 2² = 8π cm².
  4. Total = 24π + 8π = 32π cm².

Rectangle 4π cm by 6 cm, two circles of radius 2 cm; total surface area 32π cm².

Try the worksheet

Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.

  1. Build the foundation

    1.A closed cylinder has radius 3 cm and height 5 cm. Draw its net and label the rectangle dimensions and the two circles. No area calculation is required.

    Show your work on paper.

  2. Build the foundation

    2.A paper label covers only the curved side of a cylinder with radius 4 cm and height 9 cm. Find the label area exactly and using π ≈ 3.14.

    Show your work on paper.

  3. Strengthen your method

    3.A closed cylinder has diameter 10 cm and height 12 cm. Find total surface area exactly and using 3.14.

    Show your work on paper.

  4. Strengthen your method

    4.A cylindrical container is open at the top and has radius 6 cm and height 8 cm. Sketch a net showing only its surfaces and find their total area in terms of π.

    Show your work on paper.

  5. Apply and explain

    5.The rectangle in a closed cylinder net is 18π cm long and 7 cm wide. Find the cylinder radius and total surface area in terms of π.

    Show your work on paper.

  6. Apply and explain

    6.A cardboard sleeve covers the curved side of a cylinder of radius 5 cm and height 11 cm. It needs a 2 cm overlap along the wrapping direction, with no overlap added to the height. Find the rectangular cardboard area using π ≈ 3.14.

    Show your work on paper.
Download free worksheetPDF

Worked answers

Try the questions first. Then compare the reasoning, not just the final result.

Show all six worked solutions

  1. 1. Rectangle 6π cm by 5 cm; two circles of radius 3 cm.

    1. The rectangle wraps once around a circle: 2π × 3 = 6π cm.
    2. Its other dimension is the cylinder height, 5 cm.
    3. Attach two equal circular ends, each with radius 3 cm.
    Answer: closed cylinder netA rectangle and 2 circular ends. Circle radius: 3 cm. Rectangle height: 5 cm. Rectangle length equals the circumference. Drawing not to scale.r = 3 cmLength = circumferenceHeight: 5 cm2 circular ends + one curved side · not to scale
    Answer: closed cylinder net

  2. 2. 72π cm², approximately 226.08 cm².

    1. The label is a rectangle with wrapping length 2π × 4 = 8π cm.
    2. Area = 8π × 9 = 72π cm².
    3. 72 × 3.14 = 226.08 cm². No circular ends are included.
    Answer: label rectangle without end circlesA rectangle and 0 circular ends. Circle radius: 4 cm. Rectangle height: 9 cm. Rectangle length equals the circumference. Drawing not to scale.r = 4 cmLength = circumferenceHeight: 9 cm0 circular ends + one curved side · not to scale
    Answer: label rectangle without end circles

  3. 3. 170π cm², approximately 533.8 cm².

    1. Radius = 10 ÷ 2 = 5 cm.
    2. Curved area = 2π × 5 × 12 = 120π cm².
    3. Two ends = 2π × 5² = 50π cm².
    4. Total = 170π cm² ≈ 533.8 cm².
    Answer: dimensions of the closed netA rectangle and 2 circular ends. Circle radius: 5 cm. Rectangle height: 12 cm. Rectangle length equals the circumference. Drawing not to scale.r = 5 cmLength = circumferenceHeight: 12 cm2 circular ends + one curved side · not to scale
    Answer: dimensions of the closed net

  4. 4. 132π cm²: a rectangle and one circular base.

    1. Curved area = 2π × 6 × 8 = 96π cm².
    2. There is only one circular base: π × 6² = 36π cm².
    3. Total = 96π + 36π = 132π cm². An open top contributes no surface.
    Answer: open container has one circular baseA rectangle and 1 circular ends. Circle radius: 6 cm. Rectangle height: 8 cm. Rectangle length equals the circumference. Drawing not to scale.r = 6 cmLength = circumferenceHeight: 8 cm1 circular ends + one curved side · not to scale
    Answer: open container has one circular base

  5. 5. Radius 9 cm; total surface area 288π cm².

    1. The wrapping length gives 2πr = 18π, so r = 9 cm.
    2. The cylinder height is 7 cm. Curved area = 18π × 7 = 126π cm².
    3. Two ends = 2π × 9² = 162π cm².
    4. Total = 126π + 162π = 288π cm².
    Answer: recovered cylinder netA rectangle and 2 circular ends. Circle radius: 9 cm. Rectangle height: 7 cm. Rectangle length equals the circumference. Drawing not to scale.r = 9 cmLength = circumferenceHeight: 7 cm2 circular ends + one curved side · not to scale
    Answer: recovered cylinder net

  6. 6. 367.4 cm².

    1. The wrapping length without overlap is 2π × 5 = 10π cm.
    2. Add the 2 cm overlap: rectangle length = 10π + 2 cm.
    3. Area = (10π + 2) × 11 = 110π + 22 cm².
    4. Using 3.14 gives 345.4 + 22 = 367.4 cm². No end circles are needed.
    Answer: sleeve with wrapping overlapA rectangle and 0 circular ends. Circle radius: 5 cm. Rectangle height: 11 cm. Rectangle length equals the circumference plus 2 cm. Drawing not to scale.r = 5 cmLength = circumference + 2 cmHeight: 11 cmAdd 2 cm to the rectangle length0 circular ends + one curved side · not to scale
    Answer: sleeve with wrapping overlap

Mistakes worth catching

Making the net rectangle as long as the diameter.

Its wrapping length must equal the full circumference, not the distance across the circle.

Adding two ends to every question.

A closed cylinder has two ends, an open container one, and a sleeve none.

Adding overlap to both rectangle dimensions.

Follow the stated direction of the overlap; it changes only the relevant dimension.

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Skills covered

Geometry and measurement

  • Connect the rectangle in a cylinder net to the circumference and height.
  • Combine curved surfaces and circular ends for different cylinder designs.

Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.

Related practice

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Created by Gradulo · Updated September 9, 2026 · Free for personal and classroom practice.
Cylinder Nets & Surface Area Worksheets | Gradulo