1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use d...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
Problem #2 .Calculate the volume and surface area of a torus from the minor radius r and major radius R. The equation for the volume of a torus i:s and the equation for the surface area of a torus is A = 4㎡Ar Your script should read-in values for the minor radius and major radius and display the calculated values with appropriate units. The units should also be read-in. Test your program for the following two cases: . Or-5in and...
Part 4: Creating a Torus Class Write a code in C++ that does the following Add comments// for understanding please Specifications: A. Write a class declaration named Torus to find the surface area and volume of a torus. B. Define appropriate member variables. C. Define appropriate set (mutator) and get (accessor) functions. D. Use appropriate code to ask the user for input. E. Use appropriate member functions to “set” and store the input. F. Use appropriate member functions to “get”...
Integral Determine the shaded area enclosed by y 0 and the equation yr (0sxSI). 1 y=x 1 Double integral (Use polar coordinate) Find the volume of the solid bounded by the plane z-0 and the surface z r(r=x+ y,0Srsl). 1
Cartesian Equation: (x-2)^2 + y^2 = 1. This circle revolves about the y-axis, creating a torus. Consider this curve a parametric curve. Find the volume of the torus. (May use Simpson's Rule, n=10). Then find the area of the torus. (May use Simpson's Rule, n=10).
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)
can i get answer for all thses questions pllllleeeease Evaluate the double integral by first identifying it as the volume of a solid. STS- (7 - x) DA, R = {(x,y) 10 sxs 7,0 y s 6} 144 x Need Help? Read It Talk to a Tutor Calculate the iterated integral. 12 Sex + 3y dx dy 4397. 107 Х Need Help? Read It Talk to a Tutor 6. [-/1 Points) DETAILS SESSCALCET2 12.1.035. MY NOTES Find the volume of...
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4, Rʻ,...). Notation & Terminology: Use V, and S, for the "volume" and "surface area" of an n- dimensional solid sphere. Thus "Volume" is not always in cubic units, it is in units^n. So, similarly “surface area" is in units (n-1) and is the measurement of the boundary. 1. Look up & become familiar with the formulas for V, and S. Start in R', what...
please help with Q1 and 3 1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
Sketch the region and use a double integral to find the area of the region inside both the cardioid r=1+sin(theta) and r=1+cos(theta). I have worked through the problem twice and keep getting (3pi/4 - sqrt(2)). Can someone please explain how you arrive at, what they say, is the correct answer? Sketch the region and use a double integral to find its area The region inside both the cardioid r= 1 + sin 0 and the cardioid r= 1 + cosa...