Transcript Document
The Olympic Rings History • The rings were adopted in 1913. • The five rings represent the five major regions of the world: Africa, the Americas, Asia, Europe, and Oceania. • Every national flag in the world includes at least one of the five colors, which are blue, yellow, black, green, and red. Diameter and Radius • The distance across a circle through its centre is called its diameter, D. diameter, D • The radius, R of a circle is the distance from the centre of a circle to a point on the edge of the circle. radius, R • So a circle's diameter is twice as long as its radius: D = 2 × R. Circumference and Area • The distance around a circle is its circumference, C = 2 × p × R. • The area, A, of a circle is: A = p × R × R or A = p × R2 • Pi, p, is the ratio of the circumference of a circle to its diameter. p ≈ 22/7 p ≈ 3.1415926535... area, A Questions (use p = 3.14) 1. The diameter of the women’s discus is 21 cm. What is its area? 2. The area of a weight is 2000 cm2. What is its radius? 3. The radius of a men’s discus is 11 cm. What is its area? 4. The diameter of a bicycle wheel is 0.75 m. What is the area of the wheel? Questions • Find the total circumference of the outer parts of the Olympic rings. • Find the total circumference of the inner parts of the Olympic rings. • Find the total area of the Olympic rings. Use the ring dimensions below to answer the questions. Remember there are 5 rings in total. 110cm 10cm Answer to Question 1 Find the total circumference of the outer parts of the Olympic rings Circumference Diameter C=2×p×R D=2×R Circumference of one outer ring C1 = 2 × p × (D/2) = p × D C1 = 3.14 × cm = 345.4cm Circumference of five outer rings C5 = 5 × C1 = 5 × 345.4cm = 1727cm 110cm 10cm Answer to Question 2 Find the total circumference of the inner parts of the Olympic rings Circumference Diameter C=2×p×R D=2×R Diameter of the inner ring: D = 110 cm – 20 cm = 90 cm Circumference of one inner ring C1 = 2 × p × (D/2) = p × D C1 = 3.14 × 90 cm = 282.6 cm 110cm Circumference of five inner rings C5 = 5 × C1 = 5 × 282.6 cm = 1413 cm 10cm Answer to Question 3 Find the total area of the Olympic rings Area of one inner circle A(I)1= p × R(I)12 = 3.14 × (45cm)2 = 6358.5cm2 Radius of the inner ring, R(I)1= 45cm Radius of the outer ring, R(o)1= 55cm Area of one outer circle A(o)1= p × R(o)12 = 3.14 × (55cm)2 = 9498.5cm2 Area of one ring A1= A(o)-A(I)1= 9498.5cm–6358.5cm = 3140cm2 110cm Area of the five rings A5 = 5 × A1 = 5 × 3140cm2= 15700cm2 10cm Bicycle – Questions Q1. The rim of a bicycle wheel has a radius of 33 cm. What is the circumference of the rim of the wheel (to one decimal place)? Q2. The rim of a bicycle wheel has a diameter of 64cm. When the tire is mounted on the wheel, the diameter of the wheel increases as shown on the right. How much does the circumference of the bicycle wheel increase after the tire is mounted (to one decimal place)? 33cm 64cm 3cm Bicycle – Questions Q3. The wheel of Billy’s bike has a circumference of 2 m. How many meters will the bicycle travel when the wheel has made 400 revolutions? Q4. A bicycle wheel has a diameter of 75 cm. How many revolutions will the wheel make when it has rolled 1 km? Q5. A racer’s bicycle wheel has a diameter of 80 cm and makes 360 revolutions per minute. How far will the bicycle travel in 5 minutes? Note: The distance a wheel rolls in one revolution is equal to its circumference. Homework – Drawing the Olympic rings The rings are 11 blocks wide and 1 block thick (graph paper needs to be at least 37 blocks). 1. Count at least 7 blocks down and draw a horizontal line on the graph paper (the centerline for the three upper rings). 2. On the center line, count around 8 blocks. Mark a small cross (the center of ring 1). 3. From Ring 1 count 12 blocks and mark a small cross for Ring 2. 4. From Ring 2 count 12 blocks and mark a small cross for Ring 3. 5. To locate the center for Ring 4: start at the center of Ring 1, count over 6 blocks, then down 5.5 blocks. Mark a cross at this point. Homework – Drawing the Olympic rings 6. To locate the center for Ring 5: start at the center of Ring 2, count over 6 blocks, then down 5.5 blocks. Mark a cross here. 7. Set the compass to a radius of 5.5 blocks (diameter of 11 blocks). Draw the five large outer circles at each of the center points. 8. Set the compass to a radius of 4.5 blocks (diameter of 9 blocks). Draw the five small inner circles at each of the center points. 9. Erase small sections of the circles to create the illusion of a chain. 10. Darken the object lines and color the rings according to the diagram.