A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 2900 seats. The student
2 answers:
You might be interested in
Answer:
The volume is
Step-by-step explanation:
The General Slicing Method is given by
<em>Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is</em>
Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is
The key observation is that the width is the distance between the upper bounding curve and the lower bounding curve
The width of each square is given by
This means that the area of the square cross section at the point x is
The intersection points of the two bounding curves satisfy , which has solutions x = ±1.
Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is
