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  1. Problems
  2. /A square has all four corners on a circle of radius 14 cm…
EasyMathematicsHigh School (9–10)Mensuration › Areas and PerimetersNumericalBoard Exam

A square has all four corners on a circle of radius 14 cm…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A square has all four corners on a circle of radius 14 cm14\ \text{cm}14 cm. Find the area between the circle and the square. Take π=227\pi = \dfrac{22}{7}π=722​.

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

cm²
Need a reminder? The key ideaShowHide

A square with all corners on a circle of radius rrr has the area 2r22r^22r2. An equilateral triangle with all corners on the circle has the side r3r\sqrt{3}r3​ and the area 334r2\dfrac{3\sqrt{3}}{4}r^2433​​r2. The leaf of two quarter circles of radius aaa in a square of side aaa is (π2−1)a2\left(\dfrac{\pi}{2} - 1\right)a^2(2π​−1)a2.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Given. r=14 cmr = 14\ \text{cm}r=14 cm.

Step 1. The circle. 227×14×14=616 cm2\dfrac{22}{7} \times 14 \times 14 = 616\ \text{cm}^2722​×14×14=616 cm2.

Step 2. The square. The diagonal is 28 cm28\ \text{cm}28 cm, so the side is 142 cm14\sqrt{2}\ \text{cm}142​ cm and the area is 2×142=392 cm22 \times 14^2 = 392\ \text{cm}^22×142=392 cm2.

Step 3. The shaded part. 616−392=224 cm2616 - 392 = 224\ \text{cm}^2616−392=224 cm2.

Answer: 224 cm2224\ \text{cm}^2224 cm2.

Check. The exact form is (196π−392) cm2(196\pi - 392)\ \text{cm}^2(196π−392) cm2, and 196×227−392=616−392=224196 \times \dfrac{22}{7} - 392 = 616 - 392 = 224196×722​−392=616−392=224.

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  1. Circles with squares and trianglesShaded Regions and Combined Figures

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