Cylinder Surface Area Explorer

Use these printable worksheets and foldable activities to reinforce the relationships between cylinders, nets, lateral area, and total surface area.

Adjust the radius and height sliders to explore how the dimensions of a cylinder affect its lateral area and total surface area.

Click the highlight buttons to connect the cylinder, its net, and the formulas used to calculate surface area.

Zoom and drag the workspace to investigate how the unwrapped rectangle and circular bases relate to the original three-dimensional figure.

Notice that the width of the rectangle in the net is always equal to the circumference of the circular base.

Observe that the height of the rectangle matches the height of the cylinder exactly.

The total surface area consists of the lateral rectangle plus the two congruent circular bases.

Cylinder: A three-dimensional figure with two congruent circular bases connected by a curved surface.

Lateral Area: The area of the curved surface of the cylinder when unwrapped into a rectangle.

Surface Area: The total area of all faces and surfaces of a three-dimensional figure.

Circumference: The distance around a circle, calculated using \(C=2\pi r\).

Net: A two-dimensional representation that can be folded into a three-dimensional figure.

The lateral surface of a cylinder unwraps into a rectangle whose width equals the circumference of the circular base.

\(LA=(2\pi r)(h)=2\pi rh\)

The total surface area includes the lateral area plus the areas of both circular bases.

\(SA=2\pi rh+2\pi r^2\)

You may also see the lateral area written as \(LA=\pi dh\), since the circumference of a circle is also equal to \(\pi d\).

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