Sections of a cylinder, cone and ball, the sphere equation
Find the diagonal of an axial section, the radius of a section of a cone and of a ball, and read the centre and radius from a sphere equation.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- Germany: grade 10
- Ukraine: grade 11
- Russia: grade 11
Guide
This follows Ukrainian Grade 11 geometry §19–21, §23. The axial section of a cylinder is a rectangle, of a cone an isosceles triangle, of a ball a great circle. The section of a ball has r = √(R² − d²).
Common slips: adding lengths instead of using Pythagoras, taking a distance for a radius, and flipping the signs of the centre.