United University

Geometry Grade 11. Volumes of polyhedra. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 6 hours

This course offers 11th-grade students a clear and structured introduction to the volumes of polyhedra, including prisms, parallelepipeds, pyramids, and frustums. Through concise theory, guided exercises, and interactive tests for each topic, learners master the core formulas, properties, and applications of geometric volumes. The course also strengthens spatial reasoning, geometric visualization, and problem-solving skills, providing a solid foundation for further study in mathematics.

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This interactive course introduces 11th-grade students to the study of volumes of polyhedra. It provides a clear and systematic exploration of the concepts of volume, the structure of three-dimensional figures, and the methods of calculating the volumes of prisms, parallelepipeds, pyramids, and frustums of pyramids. Through theory-based lessons, step-by-step exercises, and interactive tasks, learners master the formulas, relationships, and applications associated with the volumes of geometric solids. The course develops spatial reasoning, geometric visualization, and problem-solving skills essential for advanced mathematics and real-world contexts.

Key Features of the Course

  • Interactive, step-by-step study of polyhedral volume concepts
  • Practice-oriented problem-solving with real-world applications
  • Topic-based interactive tests for self-assessment
  • Structured progression from basic definitions to advanced volume calculations
  • Exercises suitable for classroom learning and independent study
  • Fully aligned with curriculum standards in mathematics

Course Modules

Module 1: Volumes of Polyhedra

Lesson 9: Volume of a Solid. Volumes of a Prism and a Parallelepiped

  • Solve problems and complete exercises 9.1 – 9.23
  • Solve problems and complete exercises 9.24 – 9.47
  • Solve problems and complete exercises 9.48 – 9.71
  • Solve problems and complete exercises 9.72 – 9.95
  • Solve problems and complete exercises 9.96 – 9.119
  • Solve problems and complete exercises 9.120 – 9.136
  • Test your competence

Lesson 10: Volumes of a Pyramid and a Frustum of a Pyramid

  • Solve problems and complete exercises 10.1 – 10.21
  • Solve problems and complete exercises 10.22 – 10.43
  • Solve problems and complete exercises 10.44 – 10.65
  • Solve problems and complete exercises 10.66 – 10.87
  • Solve problems and complete exercises 10.88 – 10.109
  • Solve problems and complete exercises 10.110 – 10.126
  • Test your competence
  • Independent homework
  • Knowledge review tasks for §9
  • Review exercises for Section 3
  • For §9
  • For §10

Expected Learning Outcomes

  • Writes and applies formulas for calculating the volumes of parallelepipeds, prisms, pyramids, and frustums.
  • 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 strong foundation in spatial geometry through a structured combination of theory and practice. By engaging with interactive problem-solving and visualization tasks, students develop the competence to model, calculate, and interpret three-dimensional forms in both academic study and real-life applications.

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