Unrolling a Cylinder
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 38 of 62.
Peel the label off a can and lay it flat: it is a rectangle. Its height is the can's height, and its width is the distance round the can, the circumference 2×pi×r. So the curved side has area 2×pi×r×h. Add the two circle ends, pi×r^2 each.
This cylinder has radius 2 and height 5. The ends make 2 × pi × 2^2 = 8×pi, the curved side makes 2 × pi × 2 × 5 = 20×pi, and the total is 28π.
The rule is Surface area of a cylinder: SA = 2×pi×r^2 + 2×pi×r×h. An open pipe would have only the curved part, and a cup only one end: read what the question covers.
Challenge
Find the exact surface area of the cylinder, ends included: tap the solid, pick the rule, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Surface Area & Volume
1Solids and Their Parts
Faces, Edges and VerticesPrisms and CylindersPyramids and ConesHeight or Slant Height?Spheres and HemispheresRecap: Parts of Solids4Pyramids
Volume of a PyramidThe Slant HeightHeight From the SlantHeight From the VolumeRecap: Pyramids2Volume of Prisms
Volume of a CuboidVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume8Surface Area of Cylinders
Unrolling a CylinderHeight From the SurfaceRadius From the SurfaceEnough for the Volume?Recap: Cylinder Surfaces3Cylinders
Volume of a CylinderHeight From the VolumeRadius From the VolumeEnough to Find It?Recap: Cylinders6Spheres and Hemispheres
Volume of a SphereHalf a SphereRadius From the VolumeSphere in a CylinderRecap: Spheres9Pyramids and Cones Outside
Surface of a PyramidSlant Height FirstSurface of a ConeThe Cone: Slant FirstRecap: Pyramid Surfaces