Question

. The figure shows an ancient coin which was
once used in China. The coin is in the shape of
a circle of radius 3 cm with a square of sides
x cm removed from its centre. The area of each
face of the coin is 21.99 cm².
(i) Form an equation in x and show that it reduces
to 6.28-x² = 0.
(ii) Solve the equation 6.28- x2 = 0.
(iii) Find the perimeter of the square.​

Answer 1

Answer:

x=2.506 and perimeter = 10 cm.

Step-by-step explanation:

The radius of the circle is 3 cm. So, it's area will be π(3)²= 28.28 cm².

Now, the side length of the square is x cm. So, it's area will be x² cm².

(i) If we remove the square from the center of the circle, then the remaining area of the side will be 21.99 cm² ≈22 cm².

Hence, we can write that, 28.28-x²=22......... This is the equation in x. (Answer)

⇒x²-6.28=0..... reduced equation. (Answer)

(ii) If we solve the above equation, then we get, x=√6.28 =2.506 cm (Answer)

(iii) Hence, the perimeter of the square is 4x = (4×2.056) = 10.02 cm. ≈ 10 cm. (Answer)

Answer 2

Step-by-step explanation:

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