CYLINDERS AND CONES - TOTAL SURFACE AREA OF CYLINDERS AND CONES - instructional notes

Sep 18, 2026

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Lesson plan for teaching Mathematics on cylinders and cones, focusing specifically on the total surface area (TSA) of cylinders and cones. The plan covers key definitions of a cone, distinguishes right circular and oblique types, and derives formulas for TSA of cylinders (2πr(r+h)) and right circular cones (πr(l+r)). It includes worked examples using given radii, heights, and slant heights (l), applies π as 22/7 or 3.14, and concludes with an evaluation task to calculate TSA of a right circular cylinder.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Lesson Plan Overview

Classroom Details

Lesson Development

Evaluation

Conclusion

LESSON PLAN | DATE | 14/05/2025 | | --- | --- | | CLASS | J.S. 2 | | NO. IN CLASS | 80 | | SEX | MIXED | | SUBJECT | MATHEMATICS | | TOPIC | CYLINDERS AND CONES | | SUB-TOPIC | TOTAL SURFACE AREA OF CYLINDERS AND CONES | | DURATION | 2HOURS | | PERIOD | 3RD, 4TH-5TH | | TIME | 09:20 – 10:00am; 10:30 – 11:50am; | | INSTRUCTIONAL RESOURCES | Models of cylinders and cones. Nets of cylinders and cones. | | BEHAVIOURAL OBJECTIVES | At the end of the lesson, the students should be able to:
i) Describe total surface area of cylinders;
ii) Know total surface area of cones;
iii) Solving examples related to total surface area of cylinders and cones. | | PREVIOUS KNOWLEDGE | Students are conversant with cones from the previous lesson. | | REFERENCES | New General Mathematics for Junior Secondary Schools. Book 2, UBE Edition.
MAN Mathematics for Junior Secondary Schools. Book 2, UBE Edition.
New Concepts Mathematics for Junior Secondary Schools. Book 2. | | LESSON DEVELOPMENT | | | | | --- | --- | --- | --- | | PRESENTATION | TEACHER’S ACTIVITY | STUDENTS’ACTIVITIES | LEARNING
POINTS | | INTRODUCTION | Teacher introduces the lesson based on previous knowledge as thus:
A cone is a three (3D) Dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point (which forms an axis to the centre of base) called the apex and vertex. These are of two (2) types, namely: Right circular cone and Oblique circular cone. | | | | STEP I | Teacher explains to the students how to describe total surface area (TSA) of cylinders as thus:
We already know that a cylindrical shape is a combination of two (2) circular bases and rectangle like shape that joins the two bases, so, the total surface area (TSA) of this geometrical figure shall include the area of the two (2) circular faces (bases and the curved surface area (CSA)).
Hence,
The total surface area = Area of base I + Area of base II + Curved surface area (CSA).
So, TSA = πr2 + πr2 + 2πrh
= 2πr2 + 2πrh Factorize the expression above:
TSA = 2πr(r + h)
Therefore, formula to calculate the total surface area (TSA) of a cylinder is:
TSA = 2πr(r + h) | | | | STEP II | Teacher guides the students on how to know total surface area (TSA) of cones as thus:
The total surface area (TSA) of a right circular cone in equal to the sum of its lateral or curved surface area (CSA/L) and surface area of the circular face (base).
So, TSA = πrl + πr2
Factorize the expression above:
TSA = πr(l + r)
Therefore, the formula to calculate the total surface area (TSA) of a cone is:
TSA = πr(l + r) | | | | STEP III | Teacher further guides the students on how to solve questions related to total surface areas (TSA) of both cylinders and cones by applying their formulae as thus:
i) TOTAL SURFACE AREA (TSA) OF CYLINDERS | | | | | EXAMPLE
1) Emma has an old cylindrical water tank at her home. The radius is 40inches and the height is 150inches. She wants to replace it with a new one with the same dimensions. Help Emma figure out the area of the water tank.
SOLUTION
Base I r = 40inches
Curved Surface area
h = 150inches Axis Base II

The water tank is in the form of a cylinder
Formula to calculate total surface area of cylinder: TSA = 2πr(r + h), where r is radius = 40inches, his height = 150inches, π is pi and is always taken as 22/7 or 3.14.
Substitute the values in the formula:
TSA = 2πr(r + h)
TSA = 2 x 22/7 x 40(40 + 150)
= 1760(190)/7
= 384,400/7
TSA = 47,771 .43in2
Therefore, the total surface area of the water tank is 47,771.43sq.inches.
2) Find the total surface area of a cylinder with a height of 7cm and a radius of 3cm.
SOLUTION | | | | | --- | --- | --- | --- | --- | | | h = 7cm | Base I r = 3cm
Curved Surface area Axis
Base II
| | | | | Formula: TSA = 2πr(r + h), where: r = 3cm, h = 7cm
and π = 22/7 or 3.14 TSA = 2 x 22/7 x 3(3 +

FAQs

What formula is used to calculate the total surface area (TSA) of a cylinder?

The TSA of a cylinder is given by TSA = 2πr(r + h), including the two circular bases and the curved surface area.

How do you find the TSA of a right circular cone?

Use TSA = πr(l + r), where l is the slant height of the cone and r is the radius.

What is the evaluation question for checking students’ understanding?

Students are asked to find the TSA of a right circular cylinder with radius 7 cm and height 10 cm.

Sep 18, 2026

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