Area of Archway
I have this really hard question which is attached at the bottom. I am not supposed to use a calculator to solve it but I've been trying a few methods to work it out, and nothing has come nearer than calculus. I used the equation of a circle graph with radius 2 and found the integral from R to P, and multiplied it by 2.
However, I haven't actually technically 'learnt' calculus so I had to solve it with my calculator and got this:
Area from P to R =
Some devilish answer... and then there's all the tricky math involved in evaluating it. Anyways, after running it through the calculator and multiplying by 2 I get (B).
Is there any simple (non-calculus?) way to solve this? It was a question on a very time-limited test. Thanks.
Originally Posted by DivideBy0
the area will be twice the area of sector PQR minus the area of the equilateral triagle formed by their radii. (see diagram below)
so A = 2*area of sector in radians - 2*(1/2)bh
so A = 2( (1/2)r^2(pi/3)) - 2((1/2)(1)(sqrt(3))
=> A = 2(2pi/3) - sqrt(3)
=> A = 4pi/3 - sqrt(3)