Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 2nd Term
Week: 8
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Trigonometric Ratios and Applications
Topic: Solid Shapes
Subject Matter: Problems in mensuration involving – volume of cylinders and cones, surface areas of cylinder and cones.

Specific Objectives

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

Cognitive Domain:
(a) Explain the meaning of volume and surface area of cylinders and cones.
(b) Solve problems involving volumes and surface areas of cylinders and cones.
Affective Domain:
(a) Appreciate the importance of mensuration in real-life construction and design tasks.
Psychomotor Domain:
(a) Construct and analyse models of cylinders and cones using given dimensions.
Social Domain:
(a) Collaborate effectively in pairs or groups while solving mensuration problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of Work for Junior Secondary Schools
Cuemath – Solid Shapes – Definition, Types, Properties, Examples, FAQs
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Models of cylinders and cones
Chart showing formulas for volume and surface area
Rulers, compasses, and cardboard paper
Whiteboard and marker
Projector or printed diagrams

Rationale for the Lesson

This lesson equips learners with practical skills in calculating volumes and surface areas of solid shapes, which are essential for solving real-life problems involving packaging, construction, and design.

Prerequisite/Previous Knowledge

Pupils already know basic geometric shapes, radius, diameter, height, π, and have previously solved problems involving perimeter, area, and simple two-dimensional figures.

Lesson Content/Board Summary

Lesson Content

Volume and Surface Areas of Cylinders and Cones

Volume of Cylinders

A cylinder is a 3-dimensional shape with two circular bases of equal size and a curved surface. The volume measures how much space the cylinder occupies.

These include:

Formula for volume: ( V = pi r^2 h )
Example: Find the volume of a cylinder with radius 7 cm and height 10 cm.
Solution:
( V = pi r^2 h = pi (7^2)(10) = 490pi , cm^3 )

Volume of Cones

A cone is a 3-dimensional shape with one circular base and a pointed top (apex). Its volume is one-third the volume of a cylinder with the same base and height.

The following are:

Formula for volume: ( V = frac{1}{3}pi r^2 h )
Example: Find the volume of a cone with radius 5 cm and height 12 cm.
Solution:
( V = frac{1}{3}pi (5^2)(12) = 100pi , cm^3 )

Surface Area of Cylinders

The surface area of a cylinder is obtained by adding the curved surface area and the areas of the two circular bases.

These include:

Total surface area formula: ( TSA = 2pi r^2 + 2pi r h )
Example: Calculate the total surface area of a cylinder with radius 4 cm and height 9 cm.
Solution:
( TSA = 2pi (4^2) + 2pi (4)(9) = 32pi + 72pi = 104pi , cm^2 )

Surface Area of Cones

A cone’s surface area includes the curved surface area and the base area. The slant height is used when calculating the curved surface.

Examples include:

Total surface area formula: ( TSA = pi r l + pi r^2 )
Example: Calculate the total surface area of a cone with radius 3 cm and slant height 10 cm.
Solution:
( TSA = pi (3)(10) + pi (3^2) = 30pi + 9pi = 39pi , cm^2 )

Teaching Methods/Instructional Techniques

Discussion, Lecture, Explanation, Demonstration, Group Work, Visual Aids.

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher displays models of cylinders and cones and asks pupils where such shapes are seen in daily life.
Pupils’ Activity: Pupils observe the models and respond to questions.
Learning Point: Pupils become familiar with real-life examples of cylinders and cones.

Step 2: Volume of Cylinders

Time: 8 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher defines volume of cylinders and demonstrates example calculations.
Pupils’ Activity: Pupils listen and follow the worked example.
Learning Point: Pupils understand how to apply the formula for volume of cylinders.

Step 3: Volume of Cones

Time: 8 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher explains the formula for the volume of cones and solves an example on the board.
Pupils’ Activity: Pupils watch and take note of the steps.
Learning Point: Pupils learn the process of calculating cone volume.

Step 4: Surface Areas of Cylinders and Cones

Time: 10 minutes
Teaching Skill: Illustration
Teacher’s Activity: The teacher presents formulas for surface areas and explains each with diagrams and examples.
Pupils’ Activity: Pupils copy formulas and observe the examples.
Learning Point: Pupils understand formulas for surface areas of cylinders and cones.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Writing
Teacher’s Activity: The teacher guides pupils to copy the board summary correctly.
Pupils’ Activity: Pupils write the notes neatly.
Learning Point: Pupils consolidate learning through note-taking.

Step 6: Evaluation/Review

Time: 6 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define the volume of a cylinder.
State the formula for the volume of a cone.
Calculate the surface area of a cylinder with radius 3 cm and height 5 cm.
Mention the parts of a cone required to calculate surface area.
Pupils’ Activity: Pupils answer the questions orally.
Learning Point: Pupils demonstrate their understanding of the topic.

Step 7: Conclusion

Time: 3 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher summarizes the lesson and reinforces the importance of mensuration.
Pupils’ Activity: Pupils listen and ask questions where necessary.
Learning Point: Pupils recall and appreciate the key points.

Lesson Keywords

Cylinder – a solid shape with two circular bases and a curved surface.
Cone – a solid shape with one circular base and a pointed apex.
Volume – the space occupied by a solid.
Surface Area – the total area covering a 3D object.
Slant Height – the diagonal height of a cone.

Differentiation

Provide extra guidance and simplified examples for slow learners, while advanced pupils solve multi-step mensuration problems. Use visual aids to support learners who require concrete representation.

Note for teachers using this lesson plan

Always demonstrate step-by-step workings for mensuration problems. Encourage group-based problem solving and ensure pupils use correct mathematical notation.