United University

Geometry Grade 11. Volumes and surface areas of solids of revolution. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 11 hours

This interactive course for 11th-grade students explores the volumes and surface areas of solids of revolution — cylinders, cones (including frustums), and spheres. Through clear explanations, hands-on exercises, and interactive tests, learners master key geometric formulas and apply them to real-world problems. The course develops spatial reasoning, visualization, and problem-solving skills while aligning with l mathematics standards.

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This interactive course introduces 11th-grade students to the study of volumes and surface areas of solids of revolution. It provides a structured and engaging exploration of cylinders, cones (including frustums), spheres, and their surfaces. Through theory-based lessons, practical exercises, and interactive tests, learners master the key formulas, relationships, and applications of rotational solids. The course develops spatial reasoning, geometric visualization, and problem-solving skills necessary for advanced mathematical and real-life contexts.

Key Features of the Course

  • Interactive, step-by-step study of solid geometry concepts
  • Practical problem-solving with real-world applications
  • Topic-based interactive tests for self-assessment
  • Clear structure covering all major solids of revolution
  • Exercises suitable for classroom practice and independent study
  • Fully aligned with the  curriculum standards in mathematics

Course Modules

Module 1: Volumes and Surface Areas of Solids of Revolution

         Lesson 11: Volume of a Cylinder

  • Solve problems and complete exercises 11.1 – 11.17
  • Solve problems and complete exercises 11.18 – 11.33
  • Solve problems and complete exercises 11.34 – 11.50
  • Test your competence
    Lesson 12: Volume of a Cone and a Frustum
  • Solve problems and complete exercises 12.1 – 12.16
  • Solve problems and complete exercises 12.17 – 12.33
  • Solve problems and complete exercises 12.34 – 12.49
  • Solve problems and complete exercises 12.50 – 12.65
  • Test your competence
    Lesson 13: Volume of a Sphere and Its Parts
  • Solve problems and complete exercises 13.1 – 13.20
  • Solve problems and complete exercises 13.21 – 13.40
  • Solve problems and complete exercises 13.41 – 13.60
  • Solve problems and complete exercises 13.61 – 13.78
  • Test your competence
    Lesson 14: Surface Areas of Solids of Revolution
  • Solve problems and complete exercises 14.1 – 14.21
  • Solve problems and complete exercises 14.22 – 14.43
  • Solve problems and complete exercises 14.44 – 14.66
  • Solve problems and complete exercises 14.67 – 14.88
  • Solve problems and complete exercises 14.89 – 14.109
  • Solve problems and complete exercises 14.110 – 14.123
  • Test your competence
  • Independent Homework #4
  • Knowledge review tasks for §§ 11–14
  • Review exercises for Section 4
  • For §11
  • For §12
  • For §13
  • For §14
  • Special topic: Ukrainian Women in Science — Nina Virchenko

Expected Learning Outcomes

  • Writes and applies formulas for calculating the volumes of parallelepipeds, prisms, pyramids, cylinders, cones, and spheres.
  • Determines the lateral and total surface areas of cylinders, cones, and spheres.
  • Understands the concept of volume and its key properties.
  • Solves theoretical and applied problems involving volumes and surface areas of geometric solids.

Required Skills

  • Basic computer literacy and the ability to read and write.
  • Mathematical knowledge at the 11th-grade level.

This course builds a solid foundation in spatial geometry through a balanced combination of theory and practice. By engaging with interactive problem-solving and visualization tasks, students gain the competence to model, calculate, and interpret three-dimensional forms both in academic study and in real-world applications.

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