While the disk method is about stacking disks of varying radii and shape (defined by the revolution of r(x) along the x-axis at each x ), the shell method is about vertically layering rings (defined by 2πx , where x is the radius of the ring) of varying thickness and shape f(x) .
Q. What is the height of a triangular pyramid?
The slant height of the triangular pyramid is the length of a line extending from the tip of the pyramid to its base edge, forming a right angle with the edge. To determine the slant height of a triangular pyramid, square the length of one of the base triangle sides, then multiply this value by 1/12.
Table of Contents
Q. What is a cross section of a rectangular prism?
A cross section is the intersection of a plane and a three dimensional figure. A rectangular prism can have several different types of cross sections. If the cross section is perpendicular to the base, it will be the same as the lateral faces (for a rectangular prism).
Q. How do you find the cross section of a rectangle?
Cross-Sectional Area of a Rectangular Solid The volume of any rectangular solid, including a cube, is the area of its base (length times width) multiplied by its height: V = l × w × h. Therefore, if a cross section is parallel to the top or bottom of the solid, the area of the cross-section is l × w.
Q. What is the Shell method formula?
ΔV=2πxyΔx. The shell method calculates the volume of the full solid of revolution by summing the volumes of these thin cylindrical shells as the thickness Δ x /Delta x Δx goes to 0 0 0 in the limit: V = ∫ d V = ∫ a b 2 π x y d x = ∫ a b 2 π x f ( x ) d x .
Q. Why is the disk method a special case of the general slicing method?
Explanation:The slicing method deals with the elimination of the horizontal layer of the solid body . It is considered that disk method is the special case of the slicing method. Disk method consist of the slices that are used for the estimated volume of the solid body of revolution that are known as disk.
