Area (III)
Cutting a circle into many sectors and rearranging them into a near-rectangle to show area = π × radius × radius; the area from the radius or the diameter; the areas of semicircles, quarter circles and three-quarter circles; the area of a ring as the big circle minus the small one; compound shapes; the work on pi by the Chinese mathematicians Liu Hui and Zu Chongzhi; and word problems.
Key words
| Chinese | English |
|---|---|
| 圓面積 | area of a circle |
| 圓環 | ring (annulus) |
| 半圓 | semicircle |
| 四分一圓 | quarter circle |
| 組合圖形 | compound shape |
The 4 short lessons and the chapter test
Lessons are in Chinese for now.
- 圓面積公式
- 已知半徑或直徑求面積
- 半圓、四分一圓和四分三圓
- 組合圖形、圓環和應用題
- 章節測驗 (chapter test)
Sample questions (in Chinese)
Question 1把一個圓平均剪成很多份，再拼成一個近似長方形。這個長方形的長是甚麼？
- 圓周
- 圓周的一半
- 直徑
- 半徑
Answer and explanation
答案：B．圓周的一半
為甚麼？拼成的近似長方形，上下兩邊各用了圓周的一半，所以長是圓周的一半，即 π × 半徑；闊是半徑。所以圓面積 = π × 半徑 × 半徑。
Question 2求這個圓的面積。（取 π = 227）
cm²
Answer and explanation
答案：1386 cm²
為甚麼？圓的面積 = π × 半徑 × 半徑 = 227 × 21 × 21 = 1386 cm²。
Question 3求這個圓的面積。（取 π = 3.14）
cm²
Answer and explanation
答案：615.44 cm²
為甚麼？先求半徑：28 ÷ 2 = 14 cm。面積 = 3.14 × 14 × 14 = 615.44 cm²。
Question 4求這個半圓的面積。（取 π = 227）
cm²
Answer and explanation
答案：308 cm²
為甚麼？半徑 = 28 ÷ 2 = 14 cm。半圓面積 = 圓面積的一半 = 227 × 14 × 14 ÷ 2 = 308 cm²。
Based on learning unit 6M5 of the Education Bureau’s Primary Mathematics Curriculum (2017).