Question-20944

Question Number 20944 by tawa tawa last updated on 08/Sep/17

Answered by dioph last updated on 09/Sep/17

Commented by dioph last updated on 09/Sep/17

r \frac{\sqrt{3}}{2} = 7 \sqrt{3} \Rightarrow r = 14 cm

A = 4 \times (\frac{π r^{2}}{6}) - 2 \times (\frac{r^{2} \sqrt{3}}{4})

= 4 \times (\frac{22 \times 14^{2}}{7 \times 6}) - 2 \times (\frac{14^{2} \times \sqrt{3}}{4})

= \frac{1232}{3} - 98 \sqrt{3}

= (411 - \frac{1}{3}) - \sqrt{28812}

But \sqrt{28900} = 170, and

{(170 - \frac{1}{3})}^{2} = 170^{2} - \frac{340}{3} + \frac{1}{9} < 170^{2} - 113 = 27787

Hence (170 - \frac{1}{3}) < \sqrt{28812} < 170

\Rightarrow 241 - \frac{1}{3} < A < 241

So A = 241 {cm}^{2} to the nearest {cm}^{2}

Commented by tawa tawa last updated on 10/Sep/17

God bless you sir