HomeJSS 2MathematicsGeometry : Solid Shapes (Cubes, cuboids ,cylinders, cones, capacities)

Geometry : Solid Shapes (Cubes, cuboids ,cylinders, cones, capacities)

Subject : Mathematics

Class : JSS 2

Term : Second Term

Week : Week 9

Topic : Geometry : Solid Shapes (Cubes, cuboids ,cylinders, cones, capacities)

 

Previous Lesson :

Angles of Elevation and Depression

 

Objective: By the end of this lesson, students will be able to identify and describe the properties of common solid shapes including cubes, cuboids, cylinders, cones, and capacities.

Materials:

  • Visual aids such as posters or diagrams of the shapes
  • Real-life examples of the shapes (dice, shoeboxes, cans, party hats, water bottles, etc.)
  • Calculators (optional)
  • Whiteboard and markers

 

Content :

Geometry is the study of shapes, sizes, and positions of objects in space. Solid shapes are three-dimensional objects that have length, width, and height. Here are some examples of solid shapes:

  1. Cube: A cube is a solid shape that has six equal square faces. Some examples of cubes in real life are dice, Rubik’s cube, and ice cubes.
  2. Cuboid: A cuboid is a solid shape that has six rectangular faces. Some examples of cuboids in real life are bricks, shoeboxes, and books.
  3. Cylinder: A cylinder is a solid shape that has two circular faces and a curved surface. Some examples of cylinders in real life are cans, pipes, and glasses.
  4. Cone: A cone is a solid shape that has a circular base and a curved surface that tapers to a point. Some examples of cones in real life are party hats, ice cream cones, and traffic cones.
  5. Capacities: Capacities are the amount of space that a solid shape can hold. Some examples of capacities in real life are the capacity of a water bottle, the capacity of a jar, and the capacity of a bathtub.

It is important to learn about solid shapes and their properties as they are all around us in our daily lives. By understanding solid shapes, we can appreciate and understand the world better

Properties of Geometry solid shapes like cube, cuboid, cylinder, cone,

  1. Cube:
  • Has 6 faces, all of which are square and congruent.
  • Has 12 edges, all of which are of equal length.
  • Has 8 vertices, where the edges meet.
  • Examples of properties in real life: If a cube has a side length of 2 cm, then its volume is 2 x 2 x 2 = 8 cubic cm.
  1. Cuboid:
  • Has 6 faces, all of which are rectangles.
  • Has 12 edges, where opposite edges are equal in length.
  • Has 8 vertices, where the edges meet.
  • Examples of properties in real life: If a cuboid has a length of 3 cm, a width of 2 cm, and a height of 4 cm, then its volume is 3 x 2 x 4 = 24 cubic cm.
  1. Cylinder:
  • Has 3 faces – 2 circular bases and a curved surface.
  • Has no vertices, only one curved edge.
  • Examples of properties in real life: If a cylinder has a radius of 2 cm and a height of 4 cm, then its volume is 3.14 x 2 x 2 x 4 = 50.24 cubic cm.
  1. Cone:
  • Has 2 faces – a circular base and a curved surface.
  • Has one vertex, where the curved surface meets the base.
  • Examples of properties in real life: If a cone has a radius of 3 cm and a height of 5 cm, then its volume is 1/3 x 3.14 x 3 x 3 x 5 = 47.1 cubic cm.
  1. Capacities:
  • The amount of space that a solid shape can hold.
  • The capacity of a solid shape is measured in units such as milliliters or liters.
  • Examples of properties in real life: The capacity of a water bottle is 500 ml, the capacity of a jar is 1 liter, and the capacity of a bathtub is 200 liters

Worked Examples

  1. Cube: If a cube has a volume of 64 cubic units, what is the length of its edges?
  • Solution: The formula for the volume of a cube is V = a^3, where “a” is the length of its edges. Substituting V = 64, we get 64 = a^3. Taking the cube root of both sides, we get a = 4. Therefore, the length of its edges is 4 units.
  1. Cuboid: If a cuboid has a volume of 48 cubic units, a width of 3 units, and a height of 4 units, what is its length?
  • Solution: The formula for the volume of a cuboid is V = lwh, where “l” is its length, “w” is its width, and “h” is its height. Substituting V = 48, w = 3, and h = 4, we get 48 = l x 3 x 4. Solving for “l”, we get l = 4. Therefore, the length of the cuboid is 4 units.
  1. Cylinder: If a cylinder has a height of 8 units and a volume of 100 cubic units, what is the radius of its base?
  • Solution: The formula for the volume of a cylinder is V = πr^2h, where “r” is the radius of its base and “h” is its height. Substituting V = 100 and h = 8, we get 100 = πr^2 x 8. Solving for “r”, we get r = √(100/(8π)) ≈ 1.58. Therefore, the radius of its base is about 1.58 units.
  1. Cone: If a cone has a height of 12 units and a volume of 150 cubic units, what is the radius of its base?
  • Solution: The formula for the volume of a cone is V = (1/3)πr^2h, where “r” is the radius of its base and “h” is its height. Substituting V = 150 and h = 12, we get 150 = (1/3)πr^2 x 12. Solving for “r”, we get r = √(150/(4π)) ≈ 2.78. Therefore, the radius of its base is about 2.78 units.
  1. Capacities: If a cylindrical tank has a radius of 2 meters and a height of 5 meters, what is its capacity in liters?
  • Solution: The formula for the volume of a cylinder is V = πr^2h, where “r” is the radius of its base, “h” is its height, and the result is in cubic meters. Substituting r = 2 and h = 5, we get V = π x 2^2 x 5 = 20π cubic meters. Since 1 cubic meter is equal to 1000 liters, the capacity of the tank is 20π x 1000 ≈ 62,831 liters

 

Evaluation

  1. What is the formula for the volume of a cube with edge length “a”? A) V = a^3 B) V = 2a^2 C) V = 6a D) V = (4/3)πa^3
  2. What is the difference between a cube and a cuboid? A) A cube has six rectangular faces, while a cuboid has six square faces. B) A cube has all edges of equal length, while a cuboid has opposite edges of equal length. C) A cube has 12 edges, while a cuboid has 8 edges. D) A cube has no vertices, while a cuboid has 8 vertices.
  3. What is the formula for the volume of a cylinder with base radius “r” and height “h”? A) V = πr^2 B) V = (1/3)πr^2h C) V = πr^2h D) V = 2πrh
  4. What is the difference between a cone and a cylinder? A) A cone has a circular base, while a cylinder has a triangular base. B) A cone has a curved surface that tapers to a point, while a cylinder has a curved surface that does not taper. C) A cone has no vertices, while a cylinder has one vertex. D) A cone has two faces, while a cylinder has three faces.
  5. What is the formula for the volume of a pyramid with base area “B” and height “h”? A) V = Bh B) V = (1/3)Bh C) V = B^2 D) V = (1/2)Bh
  6. What is the formula for the surface area of a sphere with radius “r”? A) A = 4πr B) A = 2πr C) A = 4πr^2 D) A = 2πr^2
  7. What is the difference between a cylinder and a prism? A) A cylinder has a curved surface, while a prism has a flat surface. B) A cylinder has a circular base, while a prism has a polygonal base. C) A cylinder has two faces, while a prism has three faces. D) A cylinder has no vertices, while a prism has at least three vertices.
  8. What is the formula for the volume of a cone with base radius “r” and height “h”? A) V = πr^2h B) V = (1/3)πr^2h C) V = πr^2 D) V = 2πrh
  9. What is the difference between a pyramid and a prism? A) A pyramid has a polygonal base, while a prism has a circular base. B) A pyramid has a pointy top, while a prism has a flat top. C) A pyramid has fewer faces than a prism. D) A pyramid has one vertex, while a prism has at least three vertices.
  10. What is the formula for the surface area of a cylinder with base radius “r” and height “h”? A) A = 2πr B) A = 2πrh C) A = 2πr^2 D) A = πr^2 + 2πrh

 

Lesson Presentation

Introduction (5 minutes):

  • Begin the lesson by asking students if they have ever played with blocks or built something out of Legos. Ask them what shapes they used to create their structures. Introduce the idea of solid shapes in geometry.

Body (40 minutes):

  • Introduce the first shape: Cube. Explain the properties of a cube, including its six equal square faces, 12 edges, and 8 vertices. Show visual aids and examples of cubes in real life. Demonstrate how to calculate the volume of a cube using the formula V = a^3.
  • Repeat the process for the remaining shapes: Cuboid, Cylinder, Cone, Capacities. Explain the properties of each shape, show visual aids, and give examples of each shape in real life. Demonstrate how to calculate the volume or capacity of each shape using the appropriate formulas.
  • Ask students to work in pairs or small groups to solve some practice problems using the formulas they have learned. Circulate around the room to assist and provide guidance as needed.

Class work 

  1. What is the difference between a cube and a cuboid? A) A cube has six rectangular faces, while a cuboid has six square faces. B) A cube has all edges of equal length, while a cuboid has opposite edges of equal length. C) A cube has no vertices, while a cuboid has 8 vertices. D) A cube has 8 edges, while a cuboid has 12 edges.
  2. What is the formula for the volume of a cylinder with base radius “r” and height “h”? A) V = πr^2h B) V = 2πrh C) V = 2πr^2 D) V = (1/3)πr^2h
  3. What is the formula for the surface area of a sphere with radius “r”? A) A = 4πr B) A = 2πr C) A = 4πr^2 D) A = 2πr^2
  4. What is the difference between a cylinder and a prism? A) A cylinder has a curved surface, while a prism has a flat surface. B) A cylinder has a circular base, while a prism has a polygonal base. C) A cylinder has no vertices, while a prism has at least three vertices. D) A cylinder has two faces, while a prism has three faces.
  5. What is the formula for the volume of a cone with base radius “r” and height “h”? A) V = πr^2 B) V = 2πrh C) V = (1/3)πr^2h D) V = πr^2h
  6. What is the capacity of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm? A) 12 cm^3 B) 60 cm^3 C) 48 cm^3 D) 20 cm^3
  7. What is the radius of a cylinder with a volume of 100 cubic units and a height of 6 units? A) 5 units B) 4 units C) 3 units D) 2 units
  8. What is the difference between a pyramid and a prism? A) A pyramid has a polygonal base, while a prism has a circular base. B) A pyramid has a pointy top, while a prism has a flat top. C) A pyramid has one vertex, while a prism has at least three vertices. D) A pyramid has fewer faces than a prism.
  9. What is the formula for the volume of a sphere with radius “r”? A) V = 4/3πr^2 B) V = 4/3πr C) V = 4/3πr^3 D) V = 4πr^3
  10. What is the difference between a cone and a cylinder? A) A cone has a circular base, while a cylinder has a triangular base. B) A cone has a curved surface that tapers to a point, while a cylinder has a curved surface that does not taper. C) A cone has one vertex, where the curved surface meets the base, while a cylinder has no vertices. D) A cone has three faces, while a cylinder has two faces

Conclusion (10 minutes):

  • Recap the lesson by reviewing the properties and formulas for each shape. Ask students to share some of the real-life examples they came up with for each shape.
  • Wrap up the lesson by asking students to reflect on what they have learned and why it is important to understand solid shapes in geometry.

Assessment:

  • Observe students during the practice problems to assess their understanding of the material.
  • At the end of the lesson, give students a short quiz to test their knowledge of the shapes and formulas covered in the lesson.

Extensions:

  • Have students work in groups to create 3D models of the shapes using paper or other materials.
  • Challenge students to come up with their own examples of each shape in real life and share them with the class.
  • Provide more advanced problems that require students to use multiple formulas to calculate volumes or capacities.

Weekly Assessment

  1. What is the difference between a cube and a cuboid? A) A cube has six rectangular faces, while a cuboid has six square faces. B) A cube has all edges of equal length, while a cuboid has opposite edges of equal length. C) A cube has no vertices, while a cuboid has 8 vertices. D) A cube has 8 edges, while a cuboid has 12 edges.
  2. What is the formula for the volume of a cylinder with base radius “r” and height “h”? A) V = πr^2h B) V = 2πrh C) V = 2πr^2 D) V = (1/3)πr^2h
  3. What is the formula for the surface area of a sphere with radius “r”? A) A = 4πr B) A = 2πr C) A = 4πr^2 D) A = 2πr^2
  4. What is the difference between a cylinder and a prism? A) A cylinder has a curved surface, while a prism has a flat surface. B) A cylinder has a circular base, while a prism has a polygonal base. C) A cylinder has no vertices, while a prism has at least three vertices. D) A cylinder has two faces, while a prism has three faces.
  5. What is the formula for the volume of a cone with base radius “r” and height “h”? A) V = πr^2 B) V = 2πrh C) V = (1/3)πr^2h D) V = πr^2h
  6. What is the capacity of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm? A) 12 cm^3 B) 60 cm^3 C) 48 cm^3 D) 20 cm^3
  7. What is the radius of a cylinder with a volume of 100 cubic units and a height of 6 units? A) 5 units B) 4 units C) 3 units D) 2 units
  8. What is the difference between a pyramid and a prism? A) A pyramid has a polygonal base, while a prism has a circular base. B) A pyramid has a pointy top, while a prism has a flat top. C) A pyramid has one vertex, while a prism has at least three vertices. D) A pyramid has fewer faces than a prism.
  9. What is the formula for the volume of a sphere with radius “r”? A) V = 4/3πr^2 B) V = 4/3πr C) V = 4/3πr^3 D) V = 4πr^3
  10. What is the difference between a cone and a cylinder? A) A cone has a circular base, while a cylinder has a triangular base. B) A cone has a curved surface that tapers to a point, while a cylinder has a curved surface that does not taper. C) A cone has one vertex, where the curved surface meets the base, while a cylinder has no vertices. D) A cone has three faces, while a cylinder has two faces

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