(4) Pumping - Integrating along the yaxis. Consider a hot tub in the shape of a hemi spherical bowl with radius 3 meters buried so the open top is at ground level. Let's determine how much work would be required to pump all the water out the top of a standpipe rising vertically two meters out of the top of the hot tub. using the formula: b u; 2] g - p - D(y) - AW) d3}. where g is the magnitude of gravity (either 9.8 arm/52 E or 32 _ft/32). p is the uid mass density: Btu) is the pumping distance. and Afy) is the crosssection area. and (1.1) are the lower= upper bounds of the uid. resp. (a) Consider the image of the hot tub from the side positioned symmetric about the yaxis so the top is on the areaxis (at ground level). Also drawn is a sample rectangular slice (with thickness tip} with labels and the corresponding generic point (Ly). yaxis Height to which we pumpI 2 meters a we the ground (x-axis). (1) With the help of a. neighbor. write a brief description of y in this context. (ii) With the help of a neighbor. write a brief description of :1: in this context. (iii) Determine the length of the arrow labeled Btu). which is the distance the water needs to be pumped from the sample slice 11p and out the top of a standpipe