Lesson Notes By Weeks and Term v5 - Grade 8
Measurement: area, surface area and volume (Grade 8) – Week 1 focus
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Measurement: area, surface area and volume (Grade 8) – Week 1 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: 1
Theme: General lesson support
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This week, we're diving into the fascinating world of measurement! Specifically, we'll be focusing on area, surface area, and volume. These concepts are absolutely crucial because they're used EVERYWHERE around us.
Think about it: from figuring out how much paint you need to decorate your bedroom (area) to calculating how much water a JoJo tank can hold (volume), measurement is a fundamental skill. Knowing how to calculate area, surface area, and volume empowers you to solve practical problems, make informed decisions, and understand the world around you better.
2.1 Area: Area is the amount of two-dimensional space a shape covers. It is measured in square units (e.g., cm², m², km²).
Square: A square has four equal sides.
Its area is calculated by: Area = side × side = side² Rectangle: A rectangle has two pairs of equal sides.
Its area is calculated by: Area = length × breadth Triangle: A triangle is a three-sided shape.
Its area is calculated by: Area = ½ × base × height Remember, the height is the perpendicular distance from the base to the opposite vertex (corner).
Circle: A circle is a round shape with all points equidistant from the center.
Its area is calculated by: Area = π × radius² (where π ≈ 3.14 or 22/7) The radius is the distance from the center of the circle to any point on its edge.
Example 1: Area of a garden bed: A rectangular garden bed is 5 meters long and 2 meters wide. What is the area of the garden bed?
Solution: Area = length × breadth = 5 m × 2 m = 10 m² Example 2: Area of a triangular piece of land: A triangular piece of land has a base of 12 meters and a height of 8 meters. What is the area of the land?
Solution: Area = ½ × base × height = ½ × 12 m × 8 m = 48 m² Example 3: Area of a circular paddling pool: A circular paddling pool has a radius of 1.5 meters. Calculate its area using π = 3.
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4. Solution: Area = π × radius² = 3.14 × (1.5 m)² = 3.14 × 2.25 m² = 7.065 m² 2.2 Surface Area: Surface area is the total area of all the faces of a 3D object. It is also measured in square units (e.g., cm², m²).
Cube: A cube has six identical square faces. Surface Area = 6 × side² Rectangular Prism (Cuboid): A rectangular prism has six rectangular faces. Surface Area = 2 × (length × breadth + breadth × height + length × height)
Example 4: Surface Area of a Rubik's Cube: A Rubik's Cube has sides of 5.7 cm. Calculate its surface area.
Solution: Surface Area = 6 × side² = 6 × (5.7 cm)² = 6 × 32.49 cm² = 194.94 cm² Example 5: Surface Area of a brick: A brick is 22 cm long, 11 cm wide and 7 cm high. Calculate its surface area.
Solution: Surface Area = 2 × (length × breadth + breadth × height + length × height) = 2 × (22 cm × 11 cm + 11 cm × 7 cm + 22 cm × 7 cm) = 2 × (242 cm² + 77 cm² + 154 cm²) = 2 × (473 cm²) = 946 cm² 2.3 Volume: Volume is the amount of three-dimensional space an object occupies. It is measured in cubic units (e.g., cm³, m³, liters). Remember that 1 liter = 1000 cm³.
Cube: Volume = side × side × side = side³ Rectangular Prism (Cuboid): Volume = length × breadth × height Example 6: Volume of a sugar cube: A sugar cube has sides of 1 cm. What is its volume?
Solution: Volume = side³ = (1 cm)³ = 1 cm³ Example 7: Volume of a water tank: A rectangular water tank is 2 meters long, 1.5 meters wide, and 1 meter high. Calculate its volume in cubic meters and liters.
Solution: Volume = length × breadth × height = 2 m × 1.5 m × 1 m = 3 m³ Since 1 m³ = 1000 liters, the volume is 3 m³ × 1000 liters/m³ = 3000 liters. 2.4 Unit Conversions It's essential to know how to convert between units: 1 m = 100 cm 1 cm = 10 mm 1 m² = (100 cm)² = 10000 cm² 1 m³ = (100 cm)³ = 1000000 cm³ 1 liter = 1000 cm³ Example 8: Converting units Convert 5 m² to cm².
Solution: 5 m² = 5 * 10000 cm² = 50000 cm² Guided Practice (With Solutions)
Question 1: Calculate the area of a rectangular school field that is 80 meters long and 50 meters wide.
Solution: Area = length × breadth = 80 m × 50 m = 4000 m² The area of the school field is 4000 square meters. This is a significant area, think about how many learners can play sports there.
Question 2: A cube-shaped container has a side length of 30 cm. Calculate its volume.
Solution: Volume = side³ = (30 cm)³ = 30 cm × 30 cm × 30 cm = 27000 cm³ This volume could also be expressed as 27 liters, since 1 liter = 1000 cm³.
Question 3: A rectangular prism has a length of 10 cm, a breadth of 5 cm, and a height of 4 cm. Calculate its surface area.
Solution: Surface Area = 2 × (length × breadth + breadth × height + length × height) Surface Area = 2 × (10 cm × 5 cm + 5 cm × 4 cm + 10 cm × 4 cm) Surface Area = 2 × (50 cm² + 20 cm² + 40 cm²) Surface Area = 2 × (110 cm²) = 220 cm² Therefore, the surface area of the rectangular prism is 220 square centimeters. Imagine wrapping this prism in paper – that's how much paper you'd need.
Question 4: A circular tablecloth has a radius of 0.8 meters. Calculate the area of the tablecloth using π = 3.
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4. Solution: Area = π radius² Area = 3.14 (0.8 m)² Area = 3.14 0.64 m² Area = 2.0096 m² Therefore, the area of the tablecloth is approximately 2.01 square meters (rounded to two decimal places). Independent Practice (Questions Only) Calculate the area of a square tile with a side length of 15 cm. What is the volume of a rectangular box that is 25 cm long, 12 cm wide, and 8 cm high? A rectangular swimming pool is 10 meters long, 6 meters wide, and 2 meters deep. How much water (in liters) is needed to fill the pool completely? Calculate the surface area of a cube with a side length of 7 cm.