Lesson Notes By Weeks and Term v5 - Grade 11
Measurement: perimeter, area and volume in contexts – Week 5 focus
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Measurement: perimeter, area and volume in contexts – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 11
Term: 3rd Term
Week: 5
Theme: General lesson support
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Measurement is a fundamental skill, crucial not just in the classroom but in everyday life, especially within the South African context. From planning community gardens to calculating paint requirements for a house to understanding water usage, measurement skills are essential for informed decision-making and problem-solving. This week, we will focus on applying our knowledge of perimeter, area, and volume to real-world scenarios. Consider the prevalence of rectangular houses in townships, requiring perimeter calculations for fencing; or the importance of understanding land area for small-scale farming, vital for many South African families.
2.1 Perimeter: The perimeter is the total distance around the outside of a two-dimensional shape. It is found by adding the lengths of all the sides.
Rectangle: Perimeter = 2 x (length + width) or P = 2(l + w)
Square: Perimeter = 4 x side length or P = 4s Triangle: Perimeter = side 1 + side 2 + side 3 or P = a + b + c Circle (Circumference): Circumference = π x diameter or C = πd or C= 2πr, where π (pi) is approximately 3.
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2. Example 1: Fencing a Vegetable Garden A family in KwaZulu-Natal wants to fence their rectangular vegetable garden to protect it from animals. The garden is 8 meters long and 5 meters wide. How much fencing material do they need?
Solution: P = 2(l + w) = 2(8m + 5m) = 2(13m) = 26 meters. They need 26 meters of fencing. 2.2 Area: Area is the amount of surface a two-dimensional shape covers. It is measured in square units (e.g., square meters, square centimeters).
Rectangle: Area = length x width or A = lw Square: Area = side length x side length or A = s² Triangle: Area = 1/2 x base x height or A = (1/2)bh Circle: Area = π x radius² or A = πr², where π (pi) is approximately 3.
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2. Example 2: Painting a Wall Sipho wants to paint a wall in his room. The wall is 3 meters high and 4 meters wide. How much area does he need to paint?
Solution: A = lw = 4m x 3m = 12 square meters (12 m²). Sipho needs to paint 12 m². 2.3 Volume: Volume is the amount of space a three-dimensional object occupies. It is measured in cubic units (e.g., cubic meters, cubic centimeters) or liters.
Cube: Volume = side length x side length x side length or V = s³ Rectangular Prism: Volume = length x width x height or V = lwh Cylinder: Volume = π x radius² x height or V = πr²h, where π (pi) is approximately 3.
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2. Conversion: 1 liter (L) = 1000 cubic centimeters (cm³)
Example 3: Calculating Water Tank Capacity A cylindrical water tank has a radius of 0.7 meters and a height of 1.5 meters. What is its volume in cubic meters? Convert this volume to liters.
Solution: V = πr²h = 3.142 x (0.7m)² x 1.5m = 3.142 x 0.49 m² x 1.5m = 2.31 m³ (approximately).
Conversion to liters: 1 m³ = 1000 L, so 2.31 m³ = 2.31 x 1000 L = 2310 liters. 2.4 Unit Conversions: Being able to convert between different units is crucial for accurate calculations and problem-solving.
Here are some common conversions: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 liter (L) = 1000 milliliters (mL) 1 cubic meter (m³) = 1000 liters (L)
Example 4: Converting Units Convert 5 meters to centimeters.
Solution: 5 m * 100 cm/m = 500 cm Convert 2500 milliliters to liters.
Solution: 2500 mL * (1 L / 1000 mL) = 2.5 L 2.5 Scale Drawings: Scale drawings represent real-life objects or spaces in a smaller, proportional size. The scale indicates the relationship between the drawing's dimensions and the actual dimensions.
Example 5: Using a Scale Drawing A map has a scale of 1:50,
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0. Two towns are 8 cm apart on the map. What is the actual distance between the towns in kilometers?
Solution: The scale means that 1 cm on the map represents 50,000 cm in reality.
Actual distance in cm: 8 cm x 50,000 = 400,000 cm Convert cm to km: 400,000 cm / 100 cm/m / 1000 m/km = 4 km. The actual distance between the towns is 4 km. Guided Practice (With Solutions)
Question 1: A rectangular plot of land is 15 meters long and 10 meters wide. (a) Calculate the perimeter of the plot. (b) Calculate the area of the plot.
Solution: (a)
Perimeter: P = 2(l + w) = 2(15m + 10m) = 2(25m) = 50 meters.
Commentary: We use the formula for the perimeter of a rectangle, ensuring we add the length and width before multiplying by 2. (b)
Area: A = l x w = 15m x 10m = 150 square meters (150 m²).
Commentary: We use the formula for the area of a rectangle, simply multiplying the length and width.
Question 2: A circular swimming pool has a diameter of 7 meters. (a) Calculate the circumference of the pool. (Use π = 3.142) (b) Calculate the area of the pool. (Use π = 3.142)
Solution: (a)
Circumference: C = πd = 3.142 x 7m = 21.994 meters (approximately 22 meters).
Commentary: We use the formula for the circumference of a circle, using the given value of π and the diameter. (b)
Area: First, find the radius: r = d/2 = 7m/2 = 3.5m. Then, A = πr² = 3.142 x (3.5m)² = 3.142 x 12.25 m² = 38.485 m² (approximately 38.5 m²).
Commentary: Remember to calculate the radius before calculating the area. We square the radius and then multiply by π.
Question 3: A rectangular water tank is 2 meters long, 1.5 meters wide, and 1 meter high. (a) Calculate the volume of the water tank in cubic meters. (b) Convert the volume to liters.
Solution: (a)
Volume: V = l x w x h = 2m x 1.5m x 1m = 3 cubic meters (3 m³).
Commentary: We use the formula for the volume of a rectangular prism, multiplying length, width, and height. (b)
Conversion: 3 m³ x 1000 L/m³ = 3000 liters.
Commentary: We use the conversion factor 1 m³ = 1000 L to convert the volume from cubic meters to liters.