Check yourself: polyhedra, solids of revolution, volumes
Multiple-choice tests with options A, B, C, D on the lateral area of a prism, a cylinder and a cone, and on the volume of a ball.
- Ukraine: grade 11
- Russia: grade 11
Guide
Topic from the Ukrainian Grade 11 textbook (algebra and calculus with geometry): the self-test tasks in test form and the "Main points of the section" recaps for section 4 "Polyhedra", section 5 "Solids of revolution" and section 6 "Volumes of solids. Area of a sphere". Each test has four options, A, B, C, D, and exactly one is right.
Main formulas: the lateral area of a right prism is the perimeter of the base times the lateral edge, P · h; of a cylinder 2πrh; of a cone πrl; of a regular pyramid ½ P · a (a is the apothem). Volumes: prism V = Sh, pyramid V = ⅓Sh, cylinder V = πr²h, cone V = ⅓πr²h, ball V = ⁴⁄₃πR³; area of a sphere S = 4πR².
It is best to solve each problem first and only then pick an option. The child sees advice about the slip when they pick a wrong answer.