Area of a Sector of a Circle in Real-Life Situations

By the end of this lesson, learners should be able to

1. Apply the formula $A=\frac{\theta }{{360}^{\circ }}\pi r^2$ to solve practical sector area problems.
2. Calculate individual sector areas when circular regions are partitioned into equal divisions.

Key vocabulary

Sector area

The amount of surface enclosed by two radii and an arc of a circle.

The sector area of a circular shade subtending ${54}^{\circ }$ with radius $25\text{ cm}$ is $294.56{\text{ cm}}^2$.

Central angle

The angle formed at the centre of a circle by two radii meeting the arc.

A sector with a central angle of ${54}^{\circ }$ represents $0.15$ of the total circular area.

Subtended angle

The central angle enclosed between two radii pointing to the endpoints of an arc.

The subtended angle of ${80}^{\circ }$ defines the proportion of ground occupied by the assembly sector.

Lesson preview

Slide 1 · Calculating Sector Area using Central Angle and RadiusModel · 18 min

The area of a sector of a circle depends on the size of its central angle relative to a full turn of 360° and the total area of the circle. By multiplying the fractional turn $\frac{\theta }{{360}^{\circ }}$ by $\pi r^2$, we determine the precise surface area enclosed within the two radii and the subtended arc. This formula applies directly across physical crafts, structural design, and field layouts.

• A sector area is calculated using $A=\frac{\theta }{{360}^{\circ }}\times \pi r^2$, where $\theta$ is the central angle.
• Identify the radius $r$ and central angle $\theta$ from the given practical diagram or problem text before substituting values.
• Convert the central angle fraction $\frac{\theta }{{360}^{\circ }}$ to a simplified fraction or decimal to streamline calculations.
• State the final area using appropriate square units such as ${\text{cm}}^2$ or ${\text{m}}^2$ rounded to specified decimals.

Worked example. Identify parameters: radius $r=25\text{ cm}$ and central angle $\theta ={54}^{\circ }$. Write the sector area formula: $\text{Area}=\frac{\theta }{{360}^{\circ }}\times \pi r^2$. Substitute the known values: $\text{Area}=\frac{{54}^{\circ }}{{360}^{\circ }}\times 3.142\times {25}^2$. Simplify the angle ratio: $\frac{54}{360}=0.15$. Compute the product: $\text{Area}=0.15\times 3.142\times 625=294.5625{\text{ cm}}^2$. Answer: $294.56{\text{ cm}}^2$.

Check question: A circular solar reflector panel has a radius of $14\text{ cm}$. A sector with a central angle of ${90}^{\circ }$ is coated with non-reflective film. Calculate the area of this sector using $\pi =\frac{22}{7}$.

1. $11{\text{ cm}}^2$
2. $22{\text{ cm}}^2$
3. $154{\text{ cm}}^2$
4. $616{\text{ cm}}^2$

Show answer

$154{\text{ cm}}^2$. $\text{Area}=\frac{{90}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times {14}^2=\frac{1}{4}\times \frac{22}{7}\times 196=154{\text{ cm}}^2$.

Slide 2 · Applying Sector Area to Equal Divisions and Real ContextsPractice · 22 min

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

• Both slides with diagrams and class activities
• Teacher notes, SNE adaptations and assessment checks
• Homework and the other 11 lessons in this sub-strand

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All 12 lessons in Area of a Part of a Circle

1. 1Area of an AnnulusDetermine the area of an annulus in different situations
2. 2Area of an Annulus in Applied ContextsDetermine the area of an annulus in different situations
3. 3Area of a Sector of a Circle in Real-Life SituationsWork out the area of a sector of a circle in real-life situations
4. 4Area of a Sector of a Circle in Real-Life SituationsWork out the area of a sector of a circle in real-life situations
5. 5Area of an Annular SectorDetermine the area of an annular sector in different situations
6. 6Area of a Segment of a CircleWork out the area of a segment of a circle
7. 7Area of a Segment of a Circle in ContextWork out the area of a segment of a circle
8. 8Area of Common Region Between Two Intersecting CirclesDetermine the area of common region between two intersecting circles
9. 9Applications of Area of Parts of a CircleApply the area of a part of a circle in real-life situations
10. 10Applying Area of Parts of a Circle in Real-Life SituationsApply the area of a part of a circle in real-life situations
11. 11Exploring the Area of a Sector in Real-Life ContextsExplore the use of the area of a part of a circle in real-life situations
12. 12Applications of Area of a Part of a CircleExplore the use of the area of a part of a circle in real-life situations