PYQ Vault

Area of a sector from radius with angle, arc length or perimeter (or the reverse)

This type of question, asked 5 times: CDS 1 2019, CDS 1 2020, CDS 1 2021, CDS 1 2023, CDS 1 2025. All 5 questions below, oldest first.

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  1. Question 1

    CDS 1 2019

    28
    The area of a sector of a circle of radius 4 cm is 25.6 cm2^2. What is the radian measure of the arc of the sector ?

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  2. Question 2

    CDS 1 2020

    77
    Suppose a region is formed by removing a sector of 20∘20^\circ from a circular region of radius 30 feet. What is the area of this new region ?

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  3. Question 3

    CDS 1 2021

    73
    A sector is cut from a circle of radius 21 cm. If the length of the arc of the sector is 55 cm, then what is the area of the sector?

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  4. Question 4

    CDS 1 2023

    90
    The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. What is the area of the sector ?

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  5. Question 5

    CDS 1 2025

    84
    An arc AB of a circle subtends an angle x radian at the centre O. If the area of the sector AOB is equal to half of the square of length of arc AB, then what is x equal to ?

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