Lesson Notes By Weeks and Term v5 - Grade 8
Measurement: area, surface area and volume (Grade 8) – Week 3 focus
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Measurement: area, surface area and volume (Grade 8) – Week 3 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: 3
Theme: General lesson support
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This week, we delve deeper into the world of measurement, focusing on calculating the area of 2D shapes and the surface area and volume of 3D objects. These skills are essential, not just for Mathematics, but for practical tasks like planning a garden, estimating painting needs, or understanding the capacity of containers. In South Africa, understanding area and volume is vital for many fields, from agriculture (calculating field sizes) to construction (estimating material requirements) and even cooking (understanding recipe volumes).
Area: Area refers to the amount of two-dimensional space a shape covers. It's measured in square units (e.g., cm², m²).
Surface Area: Surface area is the total area of all the faces (surfaces) of a three-dimensional object. It's also measured in square units.
Volume: Volume refers to the amount of three-dimensional space an object occupies. It's measured in cubic units (e.g., cm³, m³). 2D Shapes & Formulas: Let's review the key formulas for area calculations: Rectangle: Area = Length × Breadth (A = l × b)
Square: Area = Side × Side (A = s²)
Triangle: Area = ½ × Base × Height (A = ½ × b × h)
Circle: Area = π × Radius² (A = πr²) (where π ≈ 3.14) 3D Shapes & Formulas: Cube: A cube has six identical square faces. Surface Area = 6 × (Side × Side) = 6s² Volume = Side × Side × Side = s³ Rectangular Prism (Box): A rectangular prism has six rectangular faces. Surface Area = 2(Length × Breadth + Length × Height + Breadth × Height) = 2(lb + lh + bh) Volume = Length × Breadth × Height = l × b × h Triangular Prism: A triangular prism has two triangular faces and three rectangular faces. Surface Area = (2 × Area of Triangle) + (Perimeter of Triangle × Length of Prism) Volume = (Area of Triangle) × Length of Prism = (½ × b × h) × l Composite Shapes: These are shapes made up of two or more simpler shapes. To find the area of a composite shape, we break it down into its simpler components, calculate the area of each component, and then add (or subtract, if there's a 'hole') the areas together.
Example 1: Area of a Composite Shape
A garden is shaped like a rectangle with a semi-circle attached to one end. The rectangle is 8m long and 5m wide. The semi-circle is attached to the 5m wide side. Calculate the total area of the garden.
Solution:
Area of the rectangle: A = l × b = 8m × 5m = 40 m²
Radius of the semi-circle: The diameter of the semi-circle is 5m, so the radius is 5m / 2 = 2.5m
Area of the full circle: A = πr² = 3.14 × (2.5m)² = 3.14 × 6.25 m² = 19.625 m²
Area of the semi-circle: A = (Area of circle) / 2 = 19.625 m² / 2 = 9.8125 m²
Total Area: Area of rectangle + Area of semi-circle = 40 m² + 9.8125 m² = 49.8125 m²
Therefore, the total area of the garden is approximately 49.81 m².