As an industrial designer you are designing a plastic bottle to contain a new soft drink product. As illustrated in an x-y coordinate system in the diagram below, the bottle is circular in cross...

Extracted text: As an industrial designer you are designing a plastic bottle to contain a new soft drink product. As illustrated in an x-y coordinate system in the diagram below, the bottle is circular in cross section, with a varying radius given by x(y) =0.0018y – 0.067y² +0.5y+4.5 (cm). (a) Given that the volume of the bottle at height y is given by V(y) = [ A(y)dy where A(y) is the area of the cross-section. Find the expression A(y)- (b) If you are required to approximate the volume at height y=10 using composite Trapezoidal rule with the number of subintervals n=43, find the upper bound error. (c) Approximate the volume at height y=10 using composite Trapezoidal rule with n=4. (d) Given the actual volume at height y=10 is 857.7864 cm², compare this volume with the estimated volume in (c).