Question

50 points
Difference of approximate area of circle using hexagon and using circle formula.Show steps.See picture

Answer 1

Answer:

$difference\hspace{0.2cm} between\hspace{0.2cm} the\hspace{0.2cm} two\hspace{0.2cm} areas\hspace{0.2cm} =\hspace{0.2cm} 9(2\sqrt{3} -\pi)$

Step-by-step explanation:

i) area of circle = $\pi \times r^{2} = 9\pi \hspace{0.1cm} where \hspace{0.1cm}r = 3.$

ii) therefore side of hexagon, $a = 2\sqrt{3}$

iii) therefore area of hexagon, $A = \frac{3\sqrt{3} }{2} a^{2} = \frac{3\sqrt{3} }{2} \times 12 = 18\sqrt{3}$

iv) difference between the two areas in iii) and i)  $=9(2\sqrt{3} -\pi)$