These are the MOST hardest questions from my book. Nobody in my class, which is an ADVANCED math honors 11 class, can get them, which is why I'm curious if it's even possible or not.
If you can answer these questions, you're definitly smarter than my whole class combined.
I'd like to know why it's that anwer because I'm curious about how to do it.
I'm clueless as to where to start. Eek!
1. Given: QR = 12 cm
<PQR = 30 degrees
Find: Area of the shaded region
2. Given: A circle is inscribed in a sector of another circle.
<A = 60 degrees, AB = 10 sqrt(3) cm
Find: Shaded area
3. A spherical tank is filled with water that is 20 ft. deep and 50 ft. wide.
What is the radius of the tank?
Note: All these are circles and a cone.
Here's another way to tackle the sphere problem using trig and a Great Circle around the center of the sphere.
A long chord (width of water surface=50) is given by:
The middle ordinate is 20 feet and given by ...
Now, we have two equations with two unknowns and we can solve for R and theta.
Solve  for , sub into  and solve for R and we get
Which agrees with TQ's method.
It's certainly easier using TQ's method, but if you're interested this is something to know.
In #2, I can't follow what that cone is supposed to be. Also, someone in advanced honors should know better than to spell as 'pie'
If I didn't make a mistake you are dealing with 2 equilateral triangles which I have coloured red and green.
And now it's your turn to show us the shaded region (Copy the sketch into Paint, pour lightgrey paint into the adequate region and upload the modified drawing again)