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Two sectors of the same circle, one angle in degrees and one in radians: ratio of areas

The same question, asked 7 times: 12 Sep 2025 S3*, 13 Sep 2025 S3*, 14 Sep 2025 S2*, 17 Sep 2025 S1*, 17 Sep 2025 S3*, 18 Sep 2025 S2*, 19 Sep 2025 S1*. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    12 Sep 2025 S3

    75
    A sector of a circle has a central angle of 120∘120^\circ and a radius of 7 cm. Another sector of the same circle has a central angle of 2π3\frac{2\pi}{3} radians. What is the ratio of the area of the first sector to the area of the second sector?

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  2. Question 2

    13 Sep 2025 S3

    75
    A sector has a central angle of 135∘135^\circ and a radius of 88 cm. Another sector of the same circle has a central angle of 3π4\frac{3\pi}{4} radians. What is the ratio of the area of the first sector to the area of the second sector?

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  3. Question 3

    14 Sep 2025 S2

    75
    A sector of a circle with a radius of 15 cm has a central angle of 45∘45^\circ. Another sector of the same circle has a central angle of π/4\pi/4 radians. What is the ratio of the area of the first sector to the area of the second sector?

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  4. Question 4

    17 Sep 2025 S1

    67
    A sector of a circle has a central angle of 60∘60^\circ and a radius of 8 cm. Another sector of the same circle has a central angle of π/3\pi/3 radians. What is the ratio of the area of the first sector to the area of the second sector?

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  5. Question 5

    17 Sep 2025 S3

    67
    A sector has a central angle of 180∘180^\circ and a radius of 12 cm. Another sector has a central angle of π2\frac{\pi}{2} radians and the same radius. What is the ratio of the area of the first sector to the area of the second sector?

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  6. Question 6

    18 Sep 2025 S2

    67
    A sector of a circle has a central angle of 120∘120^\circ and a radius of 5 cm. Another sector of the same circle has a central angle of 2π/32\pi/3 radians. What is the ratio of the area of the first sector to the area of the second sector?

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  7. Question 7

    19 Sep 2025 S1

    67
    A sector of a circle has a central angle of 60∘60^\circ and a radius of 9 cm. Another sector of the same circle has a central angle of π3\frac{\pi}{3} radians. What is the ratio of the area of the first sector to the area of the second sector?

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