Mathematics - Senior Secondary 1 - Mensuration of solid shapes (III)

Mensuration of solid shapes (III)

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TERM: 2ND TERM

WEEK: 8

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Mensuration of Solid Shapes (III)
Focus:

  • Volume of solids – cube, cuboid, cylinder, cone, prism, pyramids, frustum of cone and pyramid
  • Surface area and volume of compound shapes

 

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Recall the formulae for surface area and volume of common solid shapes.
  2. Accurately calculate the volume of cube, cuboid, cylinder, cone, prism, pyramid, and frustum.
  3. Identify and break down compound solid shapes into basic components.
  4. Solve problems involving the surface area and volume of compound solid shapes.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Problem-solving
  • Peer learning
  • Real-life applications

 

INSTRUCTIONAL MATERIALS:

  • Models of cube, cuboid, cylinder, cone, prism, pyramid
  • Household items (e.g., lampshade, bucket as frustum)
  • Measuring tape/ruler
  • Charts with volume and surface area formulae
  • Worksheets

 

PERIOD 1 & 2: Volume of Solids – Cube, Cuboid, Cylinder, Cone, Prism, Pyramids, Frustum

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Revision

Recalls the formulas for area of solid shapes: base area, lateral area, total surface area

Students recall and discuss with peers and teacher

Step 2 - Volume Formulae Introduction

Introduces and explains volume formulae: Cube: V = a³ Cuboid: V = l × b × h Cylinder: V = πr²h Cone: V = (1/3)πr²h Prism: V = Base Area × height Pyramid: V = (1/3) × Base Area × height Frustum: V = (1/3)πh(r₁² + r₂² + r₁r₂)

Students copy formulas and ask questions

Step 3 - Demonstration

Uses models of solids to demonstrate how volume is related to shape and size. Shows real-life frustum (e.g., bucket)

Students observe and relate shapes to objects around them

Step 4 - Practice

Gives examples of solids and guides students through calculations

Students practice solving problems with teacher support

NOTE ON BOARD

- Volume Formulas for Cube, Cuboid, Cylinder, Cone, Prism, Pyramid, Frustum - Emphasize π = 3.14

Students copy the notes

 

EVALUATION (5 exercises):

  1. Find the volume of a cube with side 5 cm.
  2. A cuboid has length 4 cm, breadth 3 cm, and height 2 cm. Find its volume.
  3. Find the volume of a cylinder with radius 7 cm and height 10 cm.
  4. A cone has radius 3 cm and height 4 cm. Find its volume.
  5. A frustum has radii 5 cm and 3 cm, and height 6 cm. Find its volume.

 

CLASSWORK (5 questions):

  1. Calculate the volume of a prism with base area 15 cm² and height 8 cm.
  2. A pyramid has a square base of side 6 cm and height 9 cm. Find its volume.
  3. Find the volume of a frustum with r₁ = 4 cm, r₂ = 2 cm, and h = 5 cm.
  4. Find the volume of a cylinder with radius 5 cm and height 12 cm.
  5. What is the volume of a cube with side length 9 cm?

 

ASSIGNMENT (5 tasks):

  1. Research and explain one practical use of volume in real life.
  2. Write the formula for the volume of a pyramid and explain its components.
  3. Find the volume of a cone with radius 6 cm and height 9 cm.
  4. Find the volume of a cuboid measuring 10 cm × 8 cm × 5 cm.
  5. A frustum of a cone has radii 6 cm and 4 cm, and height 10 cm. Calculate its volume.

 

PERIOD 3 & 4: Surface Area and Volume of Compound Shapes

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces compound shapes as combinations of two or more solids

Students listen and identify compound shapes

Step 2 - Decomposition

Demonstrates how to break compound shapes into basic solids (e.g., cone + cylinder, cuboid + half-sphere)

Students participate in identifying components

Step 3 - Formula Application

Teaches how to calculate total volume and surface area by adding the parts

Students copy examples and note the approach

Step 4 - Problem Solving

Solves real-life problems involving compound shapes (e.g., lampshade)

Students solve guided problems and ask questions

NOTE ON BOARD

Compound Shape Volume = Volume of Shape A + Volume of Shape B Surface Area = Add the surface areas (excluding joined faces)

Students take note and ask questions

 

EVALUATION (5 exercises):

  1. A shape is made of a cone on top of a cylinder. Find the total volume.
  2. A cuboid with a hemisphere on top – find total surface area.
  3. A compound shape has a cube and a prism joined. Find total volume.
  4. Identify the base shapes in a lamp-shaped object.
  5. What’s the difference in approach between surface area and volume of compound shapes?

 

CLASSWORK (5 questions):

  1. Calculate the volume of a cone (r = 3 cm, h = 5 cm) on top of a cylinder (r = 3 cm, h = 10 cm).
  2. Find the total surface area of a cuboid with a hemisphere attached (length = 10 cm, breadth = 6 cm, height = 8 cm; hemisphere r = 3 cm).
  3. A compound shape includes a cube (side = 6 cm) and a pyramid on top (height = 4 cm). Find total volume.
  4. Find the volume of a lampshade modeled as a frustum of a cone (r₁ = 6 cm, r₂ = 3 cm, h = 7 cm).
  5. Sketch a compound shape made from a cylinder and cone.

 

ASSIGNMENT (5 tasks):

  1. Create a diagram of a compound solid shape made from any two basic solids.
  2. Calculate the volume of a compound shape made of a prism and pyramid (base area = 30 cm² each; prism h = 10 cm, pyramid h = 6 cm).
  3. Research and write down any three real-life compound shapes.
  4. Explain how to calculate the surface area of a compound object.
  5. A bucket is modeled as a frustum of a cone. Find its volume if r₁ = 10 cm, r₂ = 6 cm, h = 12 cm.

 

PERIOD 5: Problem Solving and Review

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review

Summarizes the formulae and key concepts on volume and surface area

Students revise and recall formulas

Step 2 - Practice Questions

Gives multi-step problems combining shapes and guides students

Students solve problems and seek clarification

Step 3 - Discussion

Encourages students to share strategies for solving problems

Students explain their methods and compare answers

Step 4 - Assignment Discussion

Goes over assignment from previous lesson

Students correct mistakes and note solutions