Lesson

Title: Three-dimensional (3D) shapes

Grade: 6-a Lesson: S4-L2

Explanation: Hello students; let us learn a new topic today with concepts, examples, and questions for you to solve.

Lesson:

Definition: Cylinder

  • A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface at a fixed distance.

  • The total surface area of a cylinder is the sum of the curved surface area and the area of two circular bases. as \$"A" = 2πr^2 + 2πr"h"\$, where r is the radius, and h is the height.

  • The first part of the formula \$2πr^2\$ represents the area of the two circular bases, while the second part \$2πr"h"\$ represents the area of the lateral curved surface.

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Explanation: In this image, the cylinder has a surface area of 471.24 square units. The cylinder has a radius of 5 units and a height of 10 units. The formula used to calculate the surface area is A = 2πr² + 2πrh.

Definition: Cone

  • A cone is a three-dimensional geometric figure with a circular base and a curved surface that extends to a single point called the apex.

  • The base of the cone is a circle, and its area is calculated using the formula for the area of a circle: A = \$πr^2\$.

  • The lateral surface area of a cone is the area of the curved surface excluding the base. It is calculated using the formula: A = \$πrl\$, where r is the radius and l is the slant length.

  • Therefore, the complete formula for the surface area of a cone is: SA = \$πr^2 + πrl\$

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Explanation: The cone in this example has a surface area of 138.23 sq. units with radius 4 units and slant height 7 units (A = πr(r + l), π = 3.141).

Definition: Cube

  • A cube is a three-dimensional shape with six square faces.

  • It has eight vertices, twelve edges, and six faces, with all edges being equal.

  • The surface area (SA) of a cube is calculated by adding up the areas of all six faces. Since all the faces are identical squares, we can use the formula SA = \$6s^2\$, where s is the side length of one side of the cube.

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Explanation: In this image, the cube has a side length of 4 cm and a surface area of \$96 cm^2\$.

Definition: Cuboid

  • A cuboid, also known as a rectangular prism, has 8 vertices, 12 edges, and 6 faces, all rectangular and have angles measuring 90 degrees.

  • A cuboid’s surface area (SA) is found by summing the areas of all six faces.

  • This is expressed by the formula SA=2lw+2lh+2wh, where l, w, and h represent the cuboid’s length, width, and height.

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Explanation: In this image, the cuboid has a surface area of 148 square centimeters with the given dimensions. (Surface Area = 2lw + 2lh + 2wh, where l = 6, w = 4, and h = 5.)


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