Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate perimeter and area of composite 2D shapes.
• Calculate surface area and volume of 3D objects.
• Convert between different units of measurement.
• Solve problems involving capacity and cost.
• Estimate measurements and justify estimations.

Lesson summary

This week, we delve deeper into the fascinating world of measurement, focusing on length, area, volume, and capacity. Understanding measurement is crucial for many aspects of daily life in South Africa, from calculating the amount of paint needed for a classroom renovation project to figuring out how much water a JoJo tank can hold during water restrictions. It’s also essential for making informed decisions as consumers, such as comparing the price of two different sized containers of cooking oil. Many jobs, from construction to catering, rely heavily on these skills.

Lesson notes

2.1 Perimeter and Area of Composite Shapes: A composite shape is a shape made up of two or more simpler shapes. To find the perimeter, we simply add up the lengths of all the outside edges. For the area, we calculate the area of each individual shape and then add them together. Important

Note: Make sure all the units are the same before you start calculating. If one length is in meters and another is in centimeters, you'll need to convert them to the same unit first.

Formulas Recap: Rectangle: Area = length × width (A = l × w), Perimeter = 2(length + width) (P = 2(l + w))

Triangle: Area = ½ × base × height (A = ½ × b × h)

Circle: Area = π × radius² (A = πr²), Circumference = 2 × π × radius (C = 2πr) or π × diameter (C = πd) Remember that π (pi) is approximately 3.

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4. Example 1: A homeowner in Durban wants to build a deck in their backyard. The deck is shaped like a rectangle with a semi-circle on one end. The rectangular part is 5m long and 3m wide. The semi-circle has a diameter of 3m (the same as the width of the rectangle). Calculate the total area of the deck.

Solution: Rectangle Area: A = l × w = 5m × 3m = 15m² Semi-circle Area: A = ½ × πr². The radius is half the diameter, so r = 3m / 2 = 1.5m. A = ½ × 3.14 × (1.5m)² = ½ × 3.14 × 2.25m² ≈ 3.53m² Total Area: 15m² + 3.53m² = 18.53m² Therefore, the total area of the deck is approximately 18.53 square meters. 2.2 Surface Area and Volume of 3D Objects: Surface area is the total area of all the faces of a 3D object. Volume is the amount of space a 3D object occupies.

Formulas Recap: Rectangular Prism (Box): Surface Area = 2(lw + lh + wh), Volume = lwh Cylinder: Surface Area = 2πr² + 2πrh, Volume = πr²h Sphere: Surface Area = 4πr², Volume = (4/3)πr³ Example 2: A community in Limpopo wants to build a cylindrical water tank. The tank needs to hold 5000 liters of water. They want the tank to be 2 meters tall. What radius should the tank have? (Remember: 1 liter = 1000 cm³, and 1 m = 100 cm)

Solution: Convert liters to cm³: 5000 liters × 1000 cm³/liter = 5,000,000 cm³ Convert cm³ to m³: 5,000,000 cm³ / (100cm/m)³ = 5 m³ Cylinder Volume Formula: V = πr²h. We know V = 5m³ and h = 2m. We need to find r.

Rearrange the formula to solve for r: r² = V / (πh)

Substitute the values: r² = 5m³ / (3.14 × 2m) ≈ 0.796 m² Take the square root: r = √0.796 m² ≈ 0.89 m Therefore, the radius of the tank should be approximately 0.89 meters. 2.3 Unit Conversions: Knowing how to convert between units is essential.

Here are some common conversions: Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm Area: 1 m² = (100 cm)² = 10,000 cm² Volume: 1 m³ = (100 cm)³ = 1,000,000 cm³, 1 liter = 1000 cm³ Capacity: 1 liter = 1000 ml Example 3: A farmer in the Western Cape wants to irrigate his field. He needs to apply 5 liters of water per square meter of his field. His field is 2 hectares in size. How many liters of water does he need in total? (1 hectare = 10,000 m²)

Solution: Convert hectares to square meters: 2 hectares × 10,000 m²/hectare = 20,000 m² Calculate total water needed: 20,000 m² × 5 liters/m² = 100,000 liters Therefore, the farmer needs 100,000 liters of water in total. 2.4 Capacity and Cost: Capacity is the amount a container can hold. We often need to calculate the cost of filling containers, buying items in different sizes, or comparing prices.

Example 4: A shop sells cooking oil in two sizes: a 2-liter bottle for R45 and a 5-liter bottle for R

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0. Which is the better value for money?

Solution: Calculate the price per liter for the 2-liter bottle: R45 / 2 liters = R22.50/liter Calculate the price per liter for the 5-liter bottle: R100 / 5 liters = R20/liter Therefore, the 5-liter bottle is the better value for money because it costs less per liter. Guided Practice (With Solutions)

Question 1: A rectangular garden is 8 meters long and 5 meters wide. A path 1 meter wide is built around the outside of the garden. What is the area of the path?

Solution: Dimensions of garden including path: Length = 8m + 1m + 1m = 10m; Width = 5m + 1m + 1m = 7m Area of garden including path: A = l × w = 10m × 7m = 70m² Area of garden: A = l × w = 8m × 5m = 40m² Area of path: 70m² - 40m² = 30m² Therefore, the area of the path is 30 square meters. This question tests the understanding of how a border affects overall dimensions and how to find the area of the border.

Question 2: A cylindrical can of beans has a diameter of 7 cm and a height of 10 cm. Calculate the volume of the can.

Solution: Find the radius: Radius = Diameter / 2 = 7cm / 2 = 3.5 cm Apply the volume formula: Volume = πr²h = 3.14 × (3.5cm)² × 10cm ≈ 384.65 cm³ Therefore, the volume of the can is approximately 384.65 cubic centimeters. This tests the direct application of the cylinder volume formula.

Question 3: Convert 3.5 m³ to liters.

Solution: Recall the conversion: 1 m³ = 1000 liters Multiply: 3.5 m³ × 1000 liters/m³ = 3500 liters Therefore, 3.5 m³ is equal to 3500 liters. It emphasizes understanding and applying volume conversions.

Reference guide

• for building projects is a direct application of measurement. For example, calculating the amount of cement, sand, and bricks required for building a house or a classroom. Understanding area is crucial for tiling floors or painting walls, calculating roofing material needed, and landscaping gardens, ensuring accurate material purchases and preventing waste.
• Agriculture: Farmers use measurement to determine the area of their fields, the amount of fertilizer or pesticides needed, and the volume of water required for irrigation. They also use volume and capacity calculations to manage storage of grains and other agricultural products. Accurate measurements ensure efficient resource allocation, maximizing yields and minimizing costs.
• Cooking and Catering: Cooking and catering extensively use measurements of volume and capacity. Recipes call for specific amounts of ingredients (e.g., ml of milk, grams of flour), and caterers need to calculate the quantities of food and drink required for events. Understanding these measurements ensures consistent results and helps manage costs effectively. Consider a shisa nyama business needing to calculate the amount of wood needed for a weekend.
• Differentiation, Remediation and Extension
• Remediation (For struggling learners):
• Hands-on activities: Use physical objects like rulers, measuring tapes, and containers to help learners visualize measurements and perform conversions.