Please see attached image. I only need parts (b) and (c). Thank you! **9.3 Estimating Surface Area and Volume of a Wine Bottle**To estimate the surface area and volume of a wine bottle, the radius of the bottle is measured at different heights. The surface area, \( S \), and volume, \( V \), can be determined by the following integrals:\[ S = 2\pi \int_{0}^{L} r \, dz \]\[ V = \pi \int_{0}^{L} r^2 \, dz \]To determine the volume and surface area of the vase, use the data given below:| \( z \) (cm) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 ||--------------|----|----|----|----|----|----|----|----|----|----|| \( r \) (cm) | 10 | 11 | 11.9 | 12.4 | 13 | 13.5 | 13.8 | 14.1 | 13.6 | 12.1 || \( z \) (cm) | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | ||--------------|----|----|----|----|----|----|----|----|----|----|| \( r \) (cm) | 8.9 | 4.7 | 4.1 | 3.5 | 3.0 | 2.4 | 1.9 | 1.2 | 1.0 | |**Methods to Use:**- (a) Use the composite rectangle method.- (b) Use the composite trapezoidal method.- (c) Use the composite Simpson’s 3/8 method.**Diagram Explanation:**The diagram on the right is a cross-sectional view of the wine bottle, illustrating the varying radius \( r \) as a function of height \( z \). The diagram shows that the bottle has a wider middle section and tapers off towards the top and bottom. The axes are labeled to correspond with the \( z \) and \( r \) dimensions as provided in the table.

In mathematics, and more specifically in numerical analysis, the trapezoidal rule is a technique for approximating the definite integral. The ApproximateInt(f(x), x = a.. b, method = simpson[3/8], opts) command approximates the integral of f(x) from a to b by using Simpson's 3/8 rule. This rule is also known as Newton's 3/8 rule. The first two arguments (function expression and range) can be replaced by a definite integral.