Question

The figure à shown on ancient coin which was once used in china.the coin is in the shape of a circle of radius 3cm with a square of sides x cm removed from its center.the area of each face of coin is 7picm2.

(1)from an equatin in x and showw that itvis reduces to 2pi-x2=0.
(2)solve the equation 2pi-x2=0.
(3)find the perimeter of the square

Answer 1

(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm

Explanation:

(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²

The area of the square of x sides removed from its center is x².

The area A of the each face of the coin is thus A = 9π - x²

Since the area of each face of the coin A = 7π cm²,

then

7π = 9π - x²

9π - 7π - x² = 0

2π - x² = 0

(2) Solve the equation 2π - x² = 0

2π - x² = 0

x² = 2π

x = ±√(2π)

x = ± 2.51 cm

Since x cannot be negative, we take the positive answer.

So, x = 2.51 cm

≅ 2.5 cm

(3) Find the perimeter of the square

The perimeter of the square, p is given by p = 4x

p = 4 × 2.51 cm

= 10.04 cm

≅ 10 cm