Edexcel Mathematics (4XMAH) -Unit 1 - 4.9 Mensuration- Study Notes- New Syllabus
Edexcel Mathematics (4XMAH) -Unit 1 – 4.9 Mensuration- Study Notes- New syllabus
Edexcel Mathematics (4XMAH) -Unit 1 – 4.9 Mensuration- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A find perimeters and areas of sectors of circles (radian measure excluded)
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Sectors of Circles (Perimeter and Area)
A sector is a portion of a circle formed by two radii and an arc.
(Angles are measured in degrees. Radians are not required.)
Useful Circle Formulae
Circumference \( =2\pi r \)
Area \( =\pi r^2 \)
Arc Length of a Sector
If the angle at the centre is \( \theta^\circ \):
\( \mathrm{Arc\ length}=\dfrac{\theta}{360}\times2\pi r \)
Area of a Sector
\( \mathrm{Area}=\dfrac{\theta}{360}\times\pi r^2 \)
Perimeter of a Sector
Perimeter includes the arc and the two radii:
\( \mathrm{Perimeter}=2r+\mathrm{arc\ length} \)
Example 1:
Find the area of a sector of radius \( 7\text{ cm} \) and angle \( 60^\circ \).
▶️ Answer/Explanation
\( \mathrm{Area}=\dfrac{60}{360}\times\pi\times7^2 \)
\( =\dfrac{1}{6}\times49\pi=\dfrac{49\pi}{6} \)
\( \approx25.7\text{ cm}^2 \)
Conclusion: \( \approx25.7\text{ cm}^2 \).
Example 2:
A sector has radius \( 10\text{ cm} \) and angle \( 90^\circ \). Find the arc length.
▶️ Answer/Explanation
\( \mathrm{Arc\ length}=\dfrac{90}{360}\times2\pi\times10 \)
\( =\dfrac{1}{4}\times20\pi=5\pi \)
\( \approx15.7\text{ cm} \)
Conclusion: \( \approx15.7\text{ cm} \).
Example 3:
Find the perimeter of a sector of radius \( 5\text{ cm} \) and angle \( 120^\circ \).
▶️ Answer/Explanation
First find arc length:
\( \dfrac{120}{360}\times2\pi\times5=\dfrac{1}{3}\times10\pi=\dfrac{10\pi}{3} \)
Now perimeter:
\( P=2r+\mathrm{arc\ length} \)
\( P=10+\dfrac{10\pi}{3}\approx20.5\text{ cm} \)
Conclusion: \( \approx20.5\text{ cm} \).