The cylinder and the cone: bases and net
Find the bases of a cylinder and a cone and work out the lateral area of a cylinder from its net.
- Germany: grade 10
- Ukraine: grade 6
- Russia: grade 11
Guide
This follows the Ukrainian Year 6 book, part 2: item 25 "Cylinder. Cone. Sphere". The cylinder and the cone are solids of revolution: a cylinder comes from turning a rectangle about one side, a cone from turning a right triangle about a leg. The child turns the solid, taps its parts and unfolds the cylinder.
A cylinder has two equal bases, which are circles, and a lateral surface; the distance between the bases is the height. The net of a cylinder is a rectangle and two circles. One side of the rectangle is the circumference 2πr, the other is the height h, so the lateral area S = 2πrh. A cone has one base, a circle, and a lateral surface; it has an apex, a height and a slant height. Here π = 3.14.
The sphere and ball are not built as exercises here, but the lesson explains them.