Determine the Volume of a Solid by Integrating a Cross-Section With a Circle or Semicircle Question...
Determine the volume of a solid by integrating a cross-section with a triangle Question The solid S has a base described by the circle x' + y2 = 9. Cross sections perpendicular to the x-axis and the base are isosceles right triangles with one leg on the circular base. What is the volume of S?
please show all work & So panmog uoria ) 2. Let S bea solid whose base is a circle of radius r. Parallel cross-sections perpendicular to the base are squares. Find the volume of S. (This is #54 from section 6.2 in the textbook) Your answer should be in terms of r. & So panmog uoria ) 2. Let S bea solid whose base is a circle of radius r. Parallel cross-sections perpendicular to the base are squares. Find the...
5) The following integrals compute the volume of a solid with a known cross-section. For each integral, describe (1) the region R that serves as the base of the solid, (2) the shape of the cross- section and (3) whether the cross-sections are perpendicular to the x-axis or the y-axis. (c) (Iny)? dy
6) Set up and evaluate an integral to determine the volume of a solid whose base is the top half of a unit circle and whose cross-sections cut perpendicular to the x-axis are also semicircles 6) Set up and evaluate an integral to determine the volume of a solid whose base is the top half of a unit circle and whose cross-sections cut perpendicular to the x-axis are also semicircles
2. Find the volume of a solid whose cross section, perpendicular to the x -axis, has area given by x3 for each x in the interval a sx s b. Write your answer in terms of the areas A, M, and B corresponding, respectively, to the cross sections at x x -b. The a+b formula you've derived is known as the prismodial formula, notice that it looks very familiar. hint: recall our derivation of Simpson's rule on a single interval....
Compute the volume of the solid whose base is the unit circle x2 + y2 = 1 and whose vertical cross sections are squares. Enter your answer as a decimal to three places.
1. Given a solid whose base is a circle of radius 5 inches and each cross-section perpendicular to the base is an isosceles triangle with height 6 inches. Find the volume of the solid.
The last one was incorrect Use the general slicing method to find the volume of the following solid. The solid whose base is the region bounded by the curve y 24cos x and the x-axis on and whose 2'2 cross sections through the solid perpendicular to the x-axis are isosceles right triangles with a horizontal leg in the xy-plane and a vertical leg above the x-axis. y 24Vcos x Set up the integral that gives the volume of the solid....
11. Find the volume of the given right tetrahedron. (Hint: Consider slices perpendicular to one of the labeled edges.) 3. The solid lies between planes perpendicular to the x-axis at x= -1 and x = 1. The cross-sections perpendicular to the I-axis between these planes are squares whose bases run from the semicircle y = -VI-to the semicircle y = VI- 4. The solid lies between planes perpendicular to the x-axis at x= -1 and .x = 1. The cross-sections...
uestion 5 The base of a solid is the circle x 9. Find the volume of the solid given that the cross sections perpendicular to the x-axis are squares. а) @ 146 b) 147 e) 148 d) 144 e) 143 uestion 7 ketch the region bounded by the following curves and etermine the centroid of the region. y=x2-2x and y=5x-x2 (12) 21 7 15 21 b) 16 7 21 13 7 7 13 8' 8 Review Later Question 8 Find...