Lesson Notes By Weeks and Term v5 - Grade 8
Measurement: area, surface area and volume (Grade 8) – Week 2 focus
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Measurement: area, surface area and volume (Grade 8) – Week 2 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 8
Term: 3rd Term
Week: 2
Theme: General lesson support
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This week, we delve deeper into the exciting world of measurement, focusing on area, surface area, and volume. Understanding these concepts isn't just about passing exams; it's about empowering you to solve real-world problems every day. Imagine you're helping your family build a vegetable garden (like a food tunnel) to improve food security, or figuring out how much paint is needed to brighten up your room in your house – this knowledge will directly help you. Think about farmers calculating the amount of water a dam can hold, or builders estimating the materials needed for a construction project in your community - it all relies on these foundational concepts.
2. 1. Area Area is the amount of two-dimensional space a shape covers. We measure area in square units, such as square centimetres (cm²) or square metres (m²).
Rectangle: The area of a rectangle is calculated by multiplying its length (l) by its breadth (b): Area = l × b Square: A square is a special type of rectangle where all sides are equal. If the side length is 's', then: Area = s × s = s² Example 1: A rectangular garden plot is 5 metres long and 3 metres wide. What is its area?
Solution: Area = l × b = 5 m × 3 m = 15 m² Therefore, the area of the garden plot is 15 square metres.
Example 2: A square tile has sides of 20 cm. What is the area of the tile?
Solution: Area = s² = (20 cm)² = 400 cm² Therefore, the area of the tile is 400 square centimetres. 2.
2. Surface Area Surface area is the total area of all the faces of a three-dimensional object.
Cube: A cube has six identical square faces. If each side of the cube is 's', then the surface area is: Surface Area = 6 × s² Rectangular Prism (Cuboid): A rectangular prism has three pairs of identical rectangular faces. If the length is 'l', breadth is 'b', and height is 'h', then the surface area is: Surface Area = 2 × (l × b + l × h + b × h)
Why this formula works: l x b calculates the area of the top and bottom faces l x h calculates the area of the front and back faces b x h calculates the area of the left and right faces. We multiply by 2 to account for each face having a corresponding identical face.
Example 3: A cube has sides of 4 cm. What is its surface area?
Solution: Surface Area = 6 × s² = 6 × (4 cm)² = 6 × 16 cm² = 96 cm² Therefore, the surface area of the cube is 96 square centimetres.
Example 4: A rectangular prism is 6 cm long, 3 cm wide, and 2 cm high. What is its surface area?
Solution: Surface Area = 2 × (l × b + l × h + b × h) = 2 × (6 cm × 3 cm + 6 cm × 2 cm + 3 cm × 2 cm) = 2 × (18 cm² + 12 cm² + 6 cm²) = 2 × 36 cm² = 72 cm² Therefore, the surface area of the rectangular prism is 72 square centimetres. 2.
3. Volume Volume is the amount of three-dimensional space an object occupies. We measure volume in cubic units, such as cubic centimetres (cm³) or cubic metres (m³).
Cube: The volume of a cube is calculated by cubing its side length: Volume = s³ Rectangular Prism: The volume of a rectangular prism is calculated by multiplying its length, breadth, and height: Volume = l × b × h Think of volume as the area of the base multiplied by the height of the object.
Example 5: A cube has sides of 5 cm. What is its volume?
Solution: Volume = s³ = (5 cm)³ = 5 cm × 5 cm × 5 cm = 125 cm³ Therefore, the volume of the cube is 125 cubic centimetres.
Example 6: A rectangular prism is 8 cm long, 4 cm wide, and 3 cm high. What is its volume?
Solution: Volume = l × b × h = 8 cm × 4 cm × 3 cm = 96 cm³ Therefore, the volume of the rectangular prism is 96 cubic centimetres. 2.4 Unit Conversions It's important to be able to convert between units.
Area: 1 m = 100 cm, so 1 m² = (100 cm)² = 10,000 cm² Volume: 1 m = 100 cm, so 1 m³ = (100 cm)³ = 1,000,000 cm³ Example 7: Convert 2 m² to cm².
Solution: 2 m² = 2 × 10,000 cm² = 20,000 cm² Example 8: Convert 0.5 m³ to cm³.
Solution: 5 m³ = 0.5 × 1,000,000 cm³ = 500,000 cm³ Guided Practice (With Solutions)
Question 1: A rectangular swimming pool is 10 m long and 5 m wide. What is the area of the pool's surface?
Solution: Area = l × b = 10 m × 5 m = 50 m²
Commentary: We use the formula for the area of a rectangle since the pool is rectangular. We multiply the length and width, ensuring we include the correct units (m²).
Question 2: A cube-shaped container has sides of 30 cm. What is the surface area of the container?
Solution: Surface Area = 6 × s² = 6 × (30 cm)² = 6 × 900 cm² = 5400 cm²
Commentary: We use the formula for the surface area of a cube. We square the side length and then multiply by 6 (the number of faces on a cube).
Question 3: A rectangular prism-shaped box is 25 cm long, 12 cm wide, and 8 cm high. What is the volume of the box?
Solution: Volume = l × b × h = 25 cm × 12 cm × 8 cm = 2400 cm³
Commentary: We use the formula for the volume of a rectangular prism. We multiply the length, width, and height, making sure to include the correct units (cm³).
Question 4: Convert an area of 5 m² to cm².
Solution: 5 m² = 5 × 10,000 cm² = 50,000 cm²
Commentary: This demonstrates unit conversion. We know that 1 m² equals 10,000 cm², so we multiply the given area in m² by this conversion factor. Independent Practice (Questions Only) Calculate the area of a rectangular piece of land that is 15 m long and 8 m wide. What is the surface area of a cube with sides of 7 cm? A rectangular prism has a length of 10 cm, a width of 6 cm, and a height of 4 cm. Calculate its volume. Convert an area of 3 m² to cm². Convert a volume of 0.2 m³ to cm³. A square room has an area of 16 m². What is the length of each side of the room? A rectangular prism has a volume of 120 cm³. If the length is 5 cm and the width is 4 cm, what is the height?