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Difficulty: EasyPerimeter and Area of Plane Shapes

A sector of a circle of radius 14 cm14\text{ cm} subtends an angle of 90∘90^\circ at the centre of the circle. What is the area of the sector in cm2\text{cm}^2? (Take π=227\pi = \frac{22}{7})

Answer: 154 cm^2

Answer

The area of the sector is 154 cm2154\text{ cm}^2.
The area of a circular sector is given by Area=θ360∘×πr2\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2. Substituting θ=90∘\theta = 90^\circ, r=14 cmr = 14\text{ cm}, and π=227\pi = \frac{22}{7} yields 90360×227×142=14×616=154 cm2\frac{90}{360} \times \frac{22}{7} \times 14^2 = \frac{1}{4} \times 616 = 154\text{ cm}^2.

Step-by-Step Solution

1
Identify the formula for the area of a circular sector.
Area=θ360∘×πr2\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2
The area of a sector is proportional to the central angle it subtends relative to a full circle (360∘360^\circ).
2
Substitute the given values into the formula.
Area=90∘360∘×227×(14)2\text{Area} = \frac{90^\circ}{360^\circ} \times \frac{22}{7} \times (14)^2
Given radius r=14 cmr = 14\text{ cm}, angle θ=90∘\theta = 90^\circ, and π=227\pi = \frac{22}{7}.
3
Simplify the fraction and calculate the numerical value.
Area=14×227×196=14×22×28=22×7=154 cm2\text{Area} = \frac{1}{4} \times \frac{22}{7} \times 196 = \frac{1}{4} \times 22 \times 28 = 22 \times 7 = 154\text{ cm}^2
Simplifying 90360\frac{90}{360} yields 14\frac{1}{4} and dividing 196196 by 77 gives 2828.

Key Concept

Area of a sector of a circle
Estimated Time:45s
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Topics

Perimeter and Area of Plane Shapes

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