Class: Junior Secondary School 2 (JSS 2 / JS2)
Term: Third Term
Week: 3
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: The Pythagoras Rule: The Right-angled Triangle.
Topic: CYLINDERS AND CONES
Subject Matter: Curved surface area of cylinders, Curved surface area of cones, Total surface area of cylinders: Total surface area of cones

Specific Objectives

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

Cognitive Domain:

Define a cylinder and a cone.
State the formula for the curved surface area of a cylinder.
State the formula for the total surface area of a cylinder.
State the formula for the curved surface area of a cone.
State the formula for the total surface area of a cone.

Affective Domain:

Appreciate the importance of calculating surface areas of 3D shapes.
Show interest in solving problems involving cylinders and cones.

Psychomotor Domain:

Calculate the curved surface area of given cylinders and cones.
Calculate the total surface area of given cylinders and cones.
Solve word problems involving surface areas of cylinders and cones.

Collaborate with peers to solve problems related to cylinders and cones.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
State Unified Scheme of Work
New General Mathematics for Junior Secondary Schools 2
https://www.mathsisfun.com/geometry/cylinder.html
https://www.mathsisfun.com/geometry/cone.html

Instructional Materials

The teacher will teach this lesson with the aid of:

Models of cylinders and cones
Charts showing formulas for surface areas
Ruler and calculator

Rationale for the Lesson

This lesson helps pupils understand how to calculate the surface areas of cylinders and cones, which are common shapes in everyday life. This knowledge is important for solving practical problems in fields like engineering, construction, and packaging, and it builds a foundation for more advanced geometry concepts.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic plane shapes like circles and rectangles, their areas, and the properties of three-dimensional shapes.

Lesson Content/Board Summary

CYLINDERS AND CONES

Introduction to Cylinders and Cones

A cylinder is a 3D shape with two parallel circular bases of the same size and a curved surface connecting them. Examples include cans and pipes.

A cone is a 3D shape with a circular base and a single vertex (apex) connected to the base by a curved surface. Examples include party hats and ice cream cones.

Curved Surface Area (CSA) of a Cylinder

The curved surface area of a cylinder is the area of its side, excluding the top and bottom circular bases.

Formula: CSA = 2πrh

π (pi) ≈ 3.142 or 22/7 (a constant)
r = radius of the base
h = height of the cylinder

Example 1: A cylinder has a radius of 7 cm and a height of 10 cm. Calculate its curved surface area. (Use π = 22/7)

Solution:
Step 1: Write down the formula: CSA = 2πrh
Step 2: Substitute the values: r = 7 cm, h = 10 cm, π = 22/7
CSA = 2 × (22/7) × 7 × 10
Step 3: Calculate the area: CSA = 2 × 22 × 10 = 440 cm²
Therefore, the curved surface area is 440 cm².

Total Surface Area (TSA) of a Cylinder

The total surface area of a cylinder is the sum of its curved surface area and the areas of its two circular bases.

Formula: TSA = 2πrh + 2πr² or TSA = 2πr(h + r)

2πrh = curved surface area
2πr² = area of the two circular bases (πr² for one base)

Example 2: Using the cylinder from Example 1 (r = 7 cm, h = 10 cm), calculate its total surface area. (Use π = 22/7)

Solution:
Step 1: Write down the formula: TSA = 2πr(h + r)
Step 2: Substitute the values: r = 7 cm, h = 10 cm, π = 22/7
TSA = 2 × (22/7) × 7 × (10 + 7)
TSA = 2 × 22 × 17
Step 3: Calculate the area: TSA = 44 × 17 = 748 cm²
Therefore, the total surface area is 748 cm².

Curved Surface Area (CSA) of a Cone

The curved surface area of a cone is the area of its slanted side, excluding the circular base.

Formula: CSA = πrl

π (pi) ≈ 3.142 or 22/7
r = radius of the base
l = slant height of the cone

Note: The slant height (l), height (h), and radius (r) of a cone are related by the Pythagorean theorem: l² = h² + r².

Example 3: A cone has a radius of 3 cm and a slant height of 5 cm. Calculate its curved surface area. (Use π = 22/7)

Solution:
Step 1: Write down the formula: CSA = πrl
Step 2: Substitute the values: r = 3 cm, l = 5 cm, π = 22/7
CSA = (22/7) × 3 × 5
Step 3: Calculate the area: CSA = 330/7 ≈ 47.14 cm² (to 2 decimal places)
Therefore, the curved surface area is approximately 47.14 cm².

Total Surface Area (TSA) of a Cone

The total surface area of a cone is the sum of its curved surface area and the area of its circular base.

Formula: TSA = πrl + πr² or TSA = πr(l + r)

πrl = curved surface area
πr² = area of the circular base

Example 4: Using the cone from Example 3 (r = 3 cm, l = 5 cm), calculate its total surface area. (Use π = 22/7)

Solution:
Step 1: Write down the formula: TSA = πr(l + r)
Step 2: Substitute the values: r = 3 cm, l = 5 cm, π = 22/7
TSA = (22/7) × 3 × (5 + 3)
TSA = (22/7) × 3 × 8
TSA = 528/7
Step 3: Calculate the area: TSA ≈ 75.43 cm² (to 2 decimal places)
Therefore, the total surface area is approximately 75.43 cm².

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher displays models of a cylinder (e.g., a can) and a cone (e.g., a party hat) and asks pupils to identify them and mention where they see such shapes in real life.
Pupils’ Activity: Pupils identify the shapes and give examples of cylindrical and conical objects they know.
Learning Point: Pupils recall prior knowledge of 3D shapes and relate them to real-world objects.

Step 2: Explanation of Cylinders and their Surface Areas

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the properties of a cylinder, defines curved surface area (CSA) and total surface area (TSA), and introduces the formulas CSA = 2πrh and TSA = 2πr(h+r). The teacher explains each variable in the formulas.
Pupils’ Activity: Pupils listen attentively, copy the definitions and formulas into their notebooks, and ask questions for clarification.
Learning Point: Pupils understand the definitions and formulas for cylinder surface areas.

Step 3: Worked Examples for Cylinders

Time: 8 minutes
Teaching Skill: Problem Solving/Demonstration
Teacher’s Activity: The teacher works through Example 1 (CSA of cylinder) and Example 2 (TSA of cylinder) on the board, explaining each step clearly and ensuring correct unit usage.
Pupils’ Activity: Pupils observe the steps, participate in calculations, and copy the solved examples into their notebooks.
Learning Point: Pupils learn how to apply the formulas to calculate the surface areas of cylinders.

Step 4: Explanation of Cones and their Surface Areas

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the properties of a cone, defines curved surface area (CSA) and total surface area (TSA), and introduces the formulas CSA = πrl and TSA = πr(l+r). The teacher also explains the relationship between height, radius, and slant height (l² = h² + r²).
Pupils’ Activity: Pupils listen attentively, copy the definitions and formulas, and understand the terms ‘slant height’ and ‘height’.
Learning Point: Pupils understand the definitions and formulas for cone surface areas, including the slant height relationship.

Step 5: Worked Examples for Cones

Time: 8 minutes
Teaching Skill: Problem Solving/Demonstration
Teacher’s Activity: The teacher works through Example 3 (CSA of cone) and Example 4 (TSA of cone) on the board, emphasizing the use of slant height and the correct substitution of values.
Pupils’ Activity: Pupils follow the steps, contribute to the calculations, and copy the solved examples into their notebooks.
Learning Point: Pupils learn how to apply the formulas to calculate the surface areas of cones.

Step 6: Classwork/Practice

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher gives pupils a short classwork problem to solve individually or in pairs, for example: “A cylindrical can has a radius of 3.5 cm and a height of 8 cm. Calculate its curved surface area (Use π = 22/7).”
Pupils’ Activity: Pupils attempt to solve the given problem, applying the formulas and steps learned.
Learning Point: Pupils practice applying the formulas independently.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a cylinder and a cone.
State the formula for the curved surface area of a cylinder.
What is the formula for the total surface area of a cone?
A cone has a radius of 7 cm and a slant height of 10 cm. Calculate its curved surface area. (Use π = 22/7)

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key formulas and concepts covered in the lesson and assigns homework, which includes more practice problems on calculating surface areas of cylinders and cones.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils reinforce their understanding and prepare for independent practice.

Lesson Keywords

Cylinder – A 3D shape with two parallel circular bases and a curved surface.
Cone – A 3D shape with a circular base and a single vertex connected by a curved surface.
Radius (r) – The distance from the center to the edge of a circular base.
Height (h) – The perpendicular distance between the bases of a cylinder or from the apex to the base of a cone.
Slant height (l) – The distance from the apex of a cone to any point on the circumference of its base.
Curved Surface Area (CSA) – The area of the curved side of a cylinder or cone.
Total Surface Area (TSA) – The sum of the curved surface area and the area(s) of the base(s).
Pi (π) – A mathematical constant approximately equal to 3.142 or 22/7.

Differentiation

For pupils who grasp the concepts quickly, the teacher will provide more complex problems, such as finding the height or radius when the surface area is given. For pupils needing extra support, the teacher will provide additional guided practice with simpler numbers and visual aids, ensuring they understand each step before moving on.

Note for teachers using this lesson plan

Ensure that pupils have a clear understanding of the difference between height (h) and slant height (l) for cones. Encourage the use of appropriate units in all calculations. Emphasize the real-world applications of calculating surface areas to make the lesson more engaging and relevant.