exercise 1: Calculate the perimeter of the ellipse x^2 + 2y^ 2 = 1 to 3 decimal places

note: You may use any type of calculator or other technology to perform any necessary calculations, but you must clearly state what you are computing, what you use to compute it, and what the result is.

exercise 2:

A spherical tank of radius 5 m is filled to a height of 6 m with water. Calculate the volume of the water in the tank and simplify your final answer.

draw and label the tank and include a 2D rendering of the tank as a solid of revolution. The rendering should be a region in the xy-plane with the axis of revolution, along with any necessary quantities in the integral, and the equations that form the boundary curves, clearly labeled.