The 'Circle and Rectangle' Problem

Geometry Level 2

A circle and rectangle overlap such as the diagram given below.

We are told that the circumference of the circle is 9.38 cm 9.38 \text{ cm} , and that the circle and rectangle have an equal geometrical area.

Assuming the overlapping region (region in purple) is a quarter of both the circle and rectangle, work out the area of the shaded region in cm 2 \text{cm}^2 .

Note: Give your answer to at least three significant figures.


The answer is 1.75.

Surayyah Aziz by Surayyah Aziz , 18, United Kingdom

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1 solution

Surayyah Aziz
Aug 6, 2018

Solution: 1.75

Explanation:

  • 9.38 / π = diameter = 2.985746732

  • 1 2 \frac{1}{2} x diameter = radius ⇒ 2.985746732 / 2 = 1.492873366

  • Area of circle = π x r^2 = π x 1.492873366^2 = 0.1576087

  • 0.1576087 / 4 = 1.750394022 = Area of purple region

  • Answer is then given to 3 sig. figs = 1.75 cm^2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The rectangle is irrelevant. Why not just ask for the 1/4 of the area of the circle?

Milko Dyakov - 2 years, 10 months ago

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Hello, I apologise for the confusion. I just put the rectangle in to complicate the question a little, when actually reading the problem. As you have said, it has nothing to do with the answer, and can easily be ignored - which I hoped people would do if they had realised this. Thank you for sharing your concern, and yes the rectangle is irrelevant.

Surayyah Aziz - 2 years, 10 months ago

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