Consider the curve described by $y=\sqrt[\phantom{2}]{25-x^2}$ on the interval $-5x5.$

a$.$ Use the arc length formula to calculate the length of the curve.

b$.$ Check your solution for part a by using what you know about the circumference of a circle.

c$.$ Rotate the curve about the x axis to create the surface of a sphere. What is the surface area?

d$.$ Check your solution for part c by using what you know about the surface area of a sphere.

e$.$ Draw an illustration to support your results.