Applied Mathematics · 2nd secondary · First Term

Geometry and Measurement — Pyramid and cone

About this lesson

This unit introduces students to the concepts of nets of solids, pyramids, and cones, focusing on regular pyramids and right circular cones. It explains how flat cardboard can be folded into three-dimensional forms, and how to deduce properties of solids from their nets. The unit covers definitions, properties, and calculations involving slant height, height, base side length, and radius for regular pyramids and right circular cones, using examples and exercises. Students learn to solve real-life problems such as finding dimensions of a water tank or a tent, and they explore Euler's rule for polyhedra. By the end, students should be able to identify and describe pyramids and cones, draw their nets, calculate missing dimensions using the Pythagorean theorem, and apply these skills to practical situations.

Main topics in this lesson

  • Nets of solids
  • Regular pyramids and their properties
  • Right circular cones and their properties
  • Calculating slant height, height, and base dimensions
  • Applying geometry to real-life contexts

Key terms and vocabulary

  • net solid
  • pyramid
  • regular pyramid
  • right pyramid
  • cone
  • right circular cone
  • height
  • slant height
  • lateral face
  • lateral edge
  • base
  • vertex
  • drawer
  • axis
  • Euler's rule

Questions and answers on Geometry and Measurement — Pyramid and cone - practice and revision

Multiple choice questions on this lesson in Applied Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

مخروط دائري قائم ارتفاعه 9 سم وارتفاعه الجانبي 15 سم. ما طول نصف قطر قاعدته؟

  • 1 12 سم
  • 2 6 سم
  • 3 24 سم
  • 4 3 سم
2

هرم منتظم قاعدته مربعة طول ضلعها 20 سم، وارتفاعه 24 سم. ما طول حرفه الجانبي؟

  • 1 26 سم
  • 2 4 سم
  • 3 31 سم
  • 4 44 سم
3

خزان ماء على شكل مخروط دائري قائم ارتفاعه الجانبي 26 سم ونصف قطر قاعدته 10 سم. ما ارتفاع الخزان؟

  • 1 24 سم
  • 2 16 سم
  • 3 36 سم
  • 4 20 سم
4

هرم منتظم قاعدته مربعة طول ضلعها 18 سم، وارتفاعه الجانبي 15 سم. ما ارتفاعه؟

  • 1 12 سم
  • 2 9 سم
  • 3 3 سم
  • 4 6 سم
5

مخروط دائري قائم ارتفاعه الجانبي 10 سم ونصف قطر قاعدته 8 سم. ما ارتفاعه؟

  • 1 6 سم
  • 2 2 سم
  • 3 9 سم
  • 4 18 سم
6

هرم منتظم قاعدته مربعة طول ضلعها 24 سم، وارتفاعه 5 سم. ما طول ارتفاعه الجانبي؟

  • 1 13 سم
  • 2 12 سم
  • 3 7 سم
  • 4 19 سم

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