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

Mensuration of solid shapes (II)

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TERM: 2ND TERM

WEEK: 7
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Mensuration of Solid Shapes (II)
Focus:
i. Relationship between the sector of a circle and the surface area of a cone.
ii. Surface area of solids – cube, cuboid, cylinder, cone, prism, pyramids.

 

SPECIFIC OBJECTIVES:

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

  1. Demonstrate the relationship between a sector of a circle and the curved surface area of a cone.
  2. Recall and apply formulas for surface areas of cube, cuboid, cylinder, cone, prism, and pyramid.
  3. Identify the plane shapes that form the surfaces of solids.
  4. Solve real-life problems involving surface areas of solid shapes.

 

INSTRUCTIONAL TECHNIQUES:

  • Demonstration
  • Guided discovery
  • Question and answer
  • Group work
  • Practice exercises

 

INSTRUCTIONAL MATERIALS:

  • Cardboard papers (sectors, segments, nets)
  • Charts of 3D solids and their nets
  • Scissors, glue, rulers, markers
  • Whiteboard and diagrams

PERIOD 1 & 2: Sector of a Circle and the Curved Surface Area of a Cone

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of constructing a cone from a sector of a circle.

Students listen attentively and respond to questions.

Step 2 - Demonstration

Guides students to cut out a sector of a circle and fold it into a cone, showing how the radius of the sector becomes the slant height of the cone.

Students follow along by cutting and folding their own sectors.

Step 3 - Concept Linking

Leads students to see the relationship: Arc length of sector = circumference of base of cone. Explains how this helps derive the formula for curved surface area of cone (πrl).

Students observe and participate in drawing connections.

Step 4 - Guided Practice

Walks through an example: Given radius and slant height, find the curved surface area.

Students attempt similar problems with guidance.

 

NOTE ON BOARD:
Curved Surface Area of Cone (CSA) = π × r × l
Where:
r = radius of base,
l = slant height
Also: Arc Length of Sector = Circumference of Base = 2πr

Students copy notes and formulas into their notebooks.

 

EVALUATION (5 exercises):

  1. What part of a circle is used to form a cone?
  2. What becomes the slant height of the cone?
  3. State the formula for the curved surface area of a cone.
  4. If r = 4 cm and l = 6 cm, find the curved surface area.
  5. If the arc length of the sector is 18 cm, what is the radius of the cone’s base?

CLASSWORK (5 questions):

  1. Construct a cone from a sector of radius 7 cm and arc length 22 cm.
  2. Find the CSA of a cone with r = 5 cm and l = 10 cm.
  3. If a sector of radius 9 cm is folded into a cone with base radius 3 cm, find its slant height.
  4. Derive the CSA formula using the arc length concept.
  5. Calculate arc length if r = 7 cm and θ = 90°.

 

ASSIGNMENT (5 tasks):

  1. Describe in your own words how a cone is formed from a sector.
  2. Given a sector of radius 10 cm and arc length 31.4 cm, find the base radius of the cone.
  3. Find CSA of a cone with r = 6 cm and l = 8 cm.
  4. Create a cone using cardboard and label its parts.
  5. Why is the arc length important in forming a cone?

 

PERIOD 3 & 4: Surface Area of Solid Shapes (Cube, Cuboid, Cylinder, Cone, Prism, Pyramid)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Recaps plane shapes that make up solid shapes. Revisits area formulas for square, rectangle, triangle, and circle.

Students participate in discussion and recall area formulas.

Step 2 - Visual Aids

Shows nets and models of cube, cuboid, cylinder, cone, prism, and pyramid. Points out the component faces.

Students identify and name the shapes making up the solids.

Step 3 - Surface Area Formulas

Derives surface area formulas for each shape with examples.

Students copy formulas and follow the worked examples.

Step 4 - Guided Exercises

Provides guided problems for each solid. Encourages group discussion and solution sharing.

Students work in groups to solve surface area problems.

 

NOTE ON BOARD:

  • Cube: 6a²
  • Cuboid: 2(lb + bh + hl)
  • Cylinder: 2πr² + 2πrh
  • Cone: πr² + πrl
  • Prism: 2 × Area of base + Perimeter of base × height
  • Pyramid: Area of base + ½ × Perimeter × Slant height

Students copy notes and formulas into notebooks.

 

EVALUATION (5 exercises):

  1. Find the surface area of a cube with side 6 cm.
  2. A cuboid has dimensions 4 cm, 5 cm, and 6 cm. Find its surface area.
  3. Find the surface area of a cylinder with r = 3 cm, h = 10 cm.
  4. A cone has r = 4 cm, l = 7 cm. Find its total surface area.
  5. What is the surface area of a square-based pyramid with base 5 cm and slant height 10 cm?

 

CLASSWORK (5 questions):

  1. Calculate the surface area of a prism with base area 12 cm², perimeter 10 cm, and height 6 cm.
  2. A cone has a base radius 6 cm and slant height 9 cm. Find its surface area.
  3. A cylinder has height 12 cm and radius 5 cm. Find its total surface area.
  4. Find surface area of a cube with edge 10 cm.
  5. A pyramid has base perimeter 20 cm, slant height 8 cm, and base area 25 cm². Find total surface area.

ASSIGNMENT (5 tasks):

  1. Draw and label the net of a cuboid.
  2. Find the total surface area of a prism with base perimeter 16 cm, height 7 cm, and base area 24 cm².
  3. Write the surface area formula for a cylinder and explain each part.
  4. A cone has radius 5 cm and slant height 12 cm. Find CSA and total surface area.
  5. Why is it important to understand nets when calculating surface area?

 

PERIOD 5: Consolidation and Problem Solving (Application of Surface Area in Real Life)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Recap

Reviews formulas learned and encourages class discussion.

Students participate in recap and ask clarifying questions.

Step 2 - Application

Presents real-life problems (e.g., wrapping a box, labeling a can). Asks students to identify the shape and calculate needed surface area.

Students solve problems based on real-world contexts.

Step 3 - Class Project

Gives students group tasks to model solids and calculate surface areas.

Students present group work and explain their approach.

 

EVALUATION (5 exercises):

  1. You want to paint a cylindrical tank (r = 3 m, h = 5 m). Find the total area to be painted.
  2. A tent is shaped like a cone with radius 4 m and slant height 5 m. Find the area of the material used.
  3. Calculate the paper required to wrap a gift box (cuboid: 5 cm × 4 cm × 3 cm).
  4. A cone-shaped funnel needs to be coated. Find the surface area given r = 2 cm, l = 6 cm.
  5. A pyramid has base 6 cm², perimeter 12 cm, slant height 4 cm. Find total surface area.

 

CLASSWORK (5 questions):

  1. A cylindrical tin has radius 5 cm, height 10 cm. What is the area of the label to wrap around it?
  2. A pyramid has base perimeter 10 cm, slant height 5 cm, and base area 15 cm². Find its surface area.
  3. What is the surface area of a cube-shaped box of side 8 cm?
  4. A can is shaped like a cylinder with height 15 cm and radius 3 cm. Find the label area.
  5. A cone of radius 7 cm and slant height 24 cm is to be covered. What area of material is needed?

 

ASSIGNMENT (5 tasks):

  1. Write out the formulas for finding surface areas of cone, cube, and cuboid.
  2. Find the cost of painting a cuboid-shaped tank (5 m × 3 m × 2 m) at ₦100 per m².
  3. Explain how knowing surface area helps in packaging.
  4. Research and write one real-life use of finding surface area in construction.

A child’s toy box is shaped like a pyramid. Find the surface area if base area = 20 cm² and slant height = 8 cm.