Alan

As follows:

Here is the result for part a.  Use the same approach for part b.

Rearrange the first equation to get y = 10 - x.

Plug this into the second equation:  x^2 +(x - 10)^2 = 56

Expand this and rearrange to get a quadratic in x.  Solve for the two values of x. then substitute these back into y = 10 - x to find the corresponding two values of y.

The graph below shows that the value of k must lie between 0 and 100.  Clearly, you want the value of k that just clips the red graph at x = 50, so find the value of y on the red graph at x = 50 using the first equation, plug that into the second equation together with x = 50 and rearrange the resulting expression to find k.

Edit:  The value of x = 50 is incorrect - see below.

Use   angle = arc length/radius   to get the answer in radians.  Multiply the result by 180/pi to get the result in degrees.

Go to the online graphing calculator, Desmos:  https://www.desmos.com/calculator 

Type in

to see the graph.

See the answer here: https://web2.0calc.com/questions/the-table-shows-the-highest-daily-temperature-in#r1 to an almost identical question.  Only the temperature values in the table are different.  You should be able to use this to answer your question.

No problem!

Imagine the angle was 89° (or even 90°). Do you think the volume would still be the same?

(Incidentally, I make mistakes all the time!  That's why it's incumbent on all posters to check the answers themselves.)

As follows:  \(\frac{x}{y}+\frac{4}{3}+\frac{9}{2}=\frac{x}{y}+\frac{35}{6}\\ \frac{x}{y} \times \frac{4}{3} \times \frac{9}{2}=6\frac{x}{y}\\ \text{from which it follows that }5\frac{x}{y}=\frac{35}{6}\\ \text{or }\frac{x}{y}=\frac{7}{6}\)