I posted a problem "How Much Can a Goat Eat #2". Using a false assumption I calculated the overlapped area incorrectly. I request assistance in this regard. Please calculate the area of the green colored figure in this image. Thanks.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestyup its a good sum – Anunoy Chakraborty · 2 years, 5 months ago

Log in to reply

It looks like there are several ways to go about this, but this is my initial thought. First, we have \(AB = 3\sqrt{3}\). Thus \(\theta = \angle CAD = \cos^{-1}(\frac{\sqrt{3}}{4}) - \frac{\pi}{6}\). The area of the green region will then be the area of sector \(CAF\) minus the area of \(\Delta CAD\). This comes out to

\((\frac{1}{2})(6^{2})\theta - (\frac{1}{2})(3)(6\sin(\theta)) = 18\theta - 9\sin(\theta)\).

This "simplifies" to

\(18\cos^{-1}(\frac{\sqrt{3}}{4}) - 3\pi - (\frac{9}{8})\sqrt{3}(\sqrt{13} - 1)\),

which equals \(5.7115\) to \(4\) decimal places. – Brian Charlesworth · 2 years, 5 months ago

Log in to reply

Area of the green = Area of the sector - Area of triangle ADC

Area of the green = (34.34.../360 * Pi * 6^2) - (1/2 * 6* 1.69..)

Area of the green = 10.788573 - 5.0770656 = 5.7115074

This amount was taken to the problem "How Much Can a Goat Eat #2" and a corrected answer was obtained. – Guiseppi Butel · 2 years, 5 months ago

Log in to reply

– Brian Charlesworth · 2 years, 5 months ago

Glad we came to the same conclusion. I enjoyed the goat problem; thanks for posting it. :)Log in to reply

as i tried to solve it i got 4.9 as area of shaded region – Deepali Shankar · 2 years, 4 months ago

Log in to reply

what is the correct answer of this problem ???? – Deepali Shankar · 2 years, 4 months ago

Log in to reply

If you think that you have the correct answer please submit your calculations. – Guiseppi Butel · 2 years, 4 months ago

Log in to reply

5.748 – Mithun Mehedi Hasan · 2 years, 4 months ago

Log in to reply

– Guiseppi Butel · 2 years, 4 months ago

5.7115 Where did you err?Log in to reply

it can be solved by using integration in a very easy manner .just shift the whole diagram on a xy plane and do the integration by writing the equation . – Shubham Kumar Sah Sah · 2 years, 4 months ago

Log in to reply

The area is 8.58 – Mohammed El-Sayed · 2 years, 4 months ago

Log in to reply

– Guiseppi Butel · 2 years, 4 months ago

How did you get that answer?Log in to reply

4.92 square units – Tony Sharma · 2 years, 4 months ago

Log in to reply

49 – Rohit Dhiman · 2 years, 4 months ago

Log in to reply

Yup got 5.711 – Mohit Ahuja · 2 years, 5 months ago

Log in to reply

5.711 – Amardeep Singh · 2 years, 5 months ago

Log in to reply

wow – Alleria Windrunner Gomez · 2 years, 5 months ago

Log in to reply