suppose  we are planing to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill the tortilla to the edge with meat, cheese, and other ingredients. Our problem is to decide how to curve the tortilla in order to maximize the volume of food it can hold.    we start by placing a circular cylunder of radius r along a diameter of the tortilla and folding the tortilla around the cylinder. Let x represent the distance form the center of the tortilla to a point P on the diameter. Show that the cross-sectional area of the filled taco in the plane P perpendicular to the axis of the cylunder is A(x) = r root(16-x^2) - (1/2)r^2((r/2)root(16-x^2)) and write an expression for the volume of the filled taco.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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suppose  we are planing to make a taco from a round tortilla with diameter 8 inches by bending the tortilla so that it is shaped as if it is partially wrapped around a circular cylinder. We will fill the tortilla to the edge with meat, cheese, and other ingredients. Our problem is to decide how to curve the tortilla in order to maximize the volume of food it can hold. 

 

we start by placing a circular cylunder of radius r along a diameter of the tortilla and folding the tortilla around the cylinder. Let x represent the distance form the center of the tortilla to a point P on the diameter. Show that the cross-sectional area of the filled taco in the plane P perpendicular to the axis of the cylunder is A(x) = r root(16-x^2) - (1/2)r^2((r/2)root(16-x^2)) and write an expression for the volume of the filled taco. 

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