Question

50 points

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

Answer 1

`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√(3) -\pi)`

Explanation:

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

ii) therefore side of hexagon,
`a = 2√(3)`

iii) therefore area of hexagon,
`A = (3√(3) )/(2) a^(2) = (3√(3) )/(2) * 12 = 18√(3)`

iv) difference between the two areas in iii) and i)
`=9(2√(3) -\pi)`