Lesson Notes By Weeks and Term v5 - Grade 11
Measurement: perimeter, area and volume in contexts – Week 4 focus
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Measurement: perimeter, area and volume in contexts – Week 4 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: 4
Theme: General lesson support
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Measurement is a fundamental skill that permeates nearly every aspect of our lives. From calculating the amount of fencing needed for a garden to determining the volume of water a JoJo tank can hold, understanding perimeter, area, and volume is crucial for making informed decisions. In South Africa, these skills are particularly important in areas such as agriculture (calculating land area for planting), construction (determining materials needed for building), and even everyday tasks like budgeting for groceries based on packaging sizes. This week, we will delve into applying these measurement concepts in practical, real-world contexts.
2.1 Perimeter Perimeter is the total distance around the outside of a two-dimensional shape. It is calculated by adding the lengths of all the sides. The units of perimeter are the same as the units of length (e.g., meters, centimeters, kilometers).
Rectangle: Perimeter = 2 (length + width)
Square: Perimeter = 4 side Triangle: Perimeter = side1 + side2 + side3 Circle (Circumference): Circumference = π diameter = 2 π radius, where π (pi) is approximately 3.142 Example 1: A farmer in KwaZulu-Natal wants to fence a rectangular vegetable garden that is 15 meters long and 8 meters wide. How much fencing will he need?
Solution: Perimeter = 2 (length + width) = 2 (15 m + 8 m) = 2 * 23 m = 46 meters. He needs 46 meters of fencing.
Example 2: A circular flower bed has a diameter of 3 meters. What is the distance around the flower bed?
Solution: Circumference = π diameter = 3.142 3 m = 9.426 meters. 2.2 Area Area is the amount of surface a two-dimensional shape covers. The units of area are square units (e.g., square meters, square centimeters).
Rectangle: Area = length width Square: Area = side side = side 2 Triangle: Area = 1/2 base * height Circle: Area = π radius 2 Example 3: A painter needs to paint a rectangular wall that is 4 meters long and 2.5 meters high. What is the area of the wall that needs to be painted?
Solution: Area = length width = 4 m 2.5 m = 10 square meters (m 2 ).
Example 4: Calculate the area of a circular swimming pool with a radius of 3.5 meters.
Solution: Area = π radius 2 = 3.142 (3.5 m) 2 = 3.142 * 12.25 m 2 = 38.485 m 2 2.3 Volume Volume is the amount of space a three-dimensional object occupies. The units of volume are cubic units (e.g., cubic meters, cubic centimeters, liters, milliliters). 1 liter (L) = 1000 milliliters (ml) and 1 cm 3 = 1 ml.
Cube: Volume = side side * side = side 3 Rectangular Prism (Cuboid): Volume = length width * height Cylinder: Volume = π radius 2 * height Example 5: A JoJo tank is shaped like a cylinder. It has a radius of 0.7 meters and a height of 1.5 meters. What is the volume of the tank in cubic meters?
Solution: Volume = π radius 2 height = 3.142 (0.7 m) 2 1.5 m = 3.142 0.49 m 2 1.5 m = 2.31 m 3 Example 6: A box of washing powder is a rectangular prism with dimensions 25cm x 15cm x 10cm. What is the volume of the box in cubic centimeters? What is the volume in liters?
Solution: Volume = length width height = 25cm 15cm 10cm = 3750 cm 3 Since 1 cm 3 = 1 ml, the volume is 3750 ml. To convert to liters, divide by 1000: 3750 ml / 1000 = 3.75 liters 2.4 Composite Shapes Many real-world objects are made up of combinations of basic shapes. To find the perimeter or area of a composite shape, break it down into simpler shapes, calculate the perimeter or area of each individual shape, and then add or subtract the results as needed.
Example 7: A house plan shows a room that is a rectangle with a semicircle attached to one side. The rectangle is 5 meters long and 4 meters wide. The semicircle is attached to the 4-meter side. Calculate the area of the room.
Solution: Area of rectangle = length width = 5 m 4 m = 20 m 2 Radius of semicircle = 4 m / 2 = 2 m Area of semicircle = (1/2) π radius 2 = (1/2) 3.142 (2 m) 2 = (1/2) 3.142 4 m 2 = 6.284 m 2 Total area = area of rectangle + area of semicircle = 20 m 2 + 6.284 m 2 = 26.284 m 2 Guided Practice (With Solutions)
Question 1: A township resident wants to tile their rectangular kitchen floor. The kitchen is 3.5 meters long and 2.8 meters wide. Calculate the area of the kitchen floor.
Solution: Area = length width = 3.5 m 2.8 m = 9.8 m 2 . The area of the kitchen floor is 9.8 square meters.
Question 2: A cylindrical water tank has a diameter of 1.2 meters and a height of 1.8 meters. Calculate the volume of the water tank in cubic meters.
Solution: Radius = diameter / 2 = 1.2 m / 2 = 0.6 m Volume = π radius 2 height = 3.142 (0.6 m) 2 1.8 m = 3.142 0.36 m 2 1.8 m = 2.036 m 3 . The volume of the tank is approximately 2.036 cubic meters.
Question 3: A rectangular plot of land is 40 meters long and 25 meters wide. A farmer wants to put a fence around the plot. What is the length of the fence required?
Solution: Perimeter = 2 (length + width) = 2 (40 m + 25 m) = 2 * 65 m = 130 m. The farmer needs 130 meters of fencing.
Question 4: A garden is shaped like a triangle. The base of the triangle is 8 meters and the height is 6 meters. What is the area of the garden?
Solution: Area = (1/2) base height = (1/2) 8 m 6 m = 24 m 2 . The area of the garden is 24 square meters. Independent Practice (Questions Only) A school sports field is a rectangle 100 meters long and 60 meters wide. What is the perimeter of the field? Calculate the area of a circular table with a diameter of 1.5 meters. A rectangular swimming pool is 8 meters long, 4 meters wide, and 1.5 meters deep. How much water (in cubic meters) is needed to fill the pool completely? A cylindrical tin of paint has a radius of 7 cm and a height of 15 cm.