Note: Both problems will be solved by a bracketing method and an open method. Whichever bracketing or open method used for one problem should not be used for other problem. By the end, all $4$ root finding methods will be used. In excel pls

Problem $1$: According to Archimedes principle, the buoyancy force is equal to the weight of fluid displaced by the submerged portion of an object. For the sphere depicted in figure, use a bracketing method and an open method you learned in root finding chapter to determine the height $h$ of the portion that is above water. Employ the following values for your computation: radius of sphere: $r=1\mathrm{.}25m,$ density of sphere: ${}_s=450k\frac{g}{m}3$ and density of water: ${}_w=1000k\frac{g}{m}3.$ Note that the volume of the above$-$water portion of the sphere can be computed with $V=\frac{h^2(3r-h)}{3}$