EQII $(20$ points$)$ You design a simple load cell using an apple as shown below to determine the weight of a bag of corn starch. The modulus of elasticity and Poisson's ratio of the apple are $5$ MPa $,$ and $0\mathrm{.}4,$ respectively. The apple has a perfect spherical shape with a diameter of $10$ cm $.$ The distance between the flat board and counter top decreases from $100$ mm to $98$ mm when the bag of the corn starch is placed on the top of the flat board.

$(1)(10$ points$)$ What is the mass of the corn starch in kilograms? $($The mass of the flat board is negligible.$)$ Weight $(F)=$ mass $(m)x$ gravity $(9\mathrm{.}81\frac{N}{k}g)$

$(2)(10$ points$)$ What is the contact area of the apple with the top board?