Find the volume of the torus formed when a circle of radius 2 centered at (3, 0)
Question:
Find the volume of the torus formed when a circle of radius 2 centered at (3, 0) is revolved about the y-axis. Use the shell method. You may need a computer algebra system or table of integrals to evaluate the integral.
- 3- х
Step by Step Answer:
V 2 2 34 x 3 4 x dx 24 FS v 4x dx 24 24 Th...View the full answer
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
Use Pappus's Theorem to find the volume of the torus obtained when the region inside the circle x2 + y2 = a2 is revolved about the line x = 2a.
-
Consider the region R bounded by the graph of f(x) = 1/x + 2 and the x-axis on the interval [0, 3]. a. Find the volume of the solid formed when R is revolved about the x-axis. b. Find the volume of...
-
Find the volume of the solid torus formed when the circle of radius 4 centered at (0, 6) is revolved about the x-axis.
-
Hrishi is a senior executive for a large manufacturing company in Mississauga Ontario where he has been employed for the past 10 years and his annual salary is $250,000 including bonus. He is 47...
-
Suppose the address of an end system on the Internet is quoted as 134.48.4.122. What is the 32-bit address in hexadecimal notation?
-
A manufacturer of heavy truck engines must develop an aggregate production plan, given the following demand forecasts for engines. The company currently has 13 workers and makes 130 engines per...
-
What is the purpose of practice aids in forensic and valuation services?
-
The post-closing trial balance of Russo Corporation at December 31, 2014, contains the following stockholders equity accounts. Preferred Stock (15,000 shares issued) ........... $ 750,000 Common...
-
Implement the Boolean function F(A.B.C.D) - (0,1,3,4,8,9,15) with a. a multiplexer b. a decoder Question 2 Draw the NAND gate representation of G A+ B'C' + DC. [10 marks] [5 marks] [5 marks]
-
One of the biggest purchases we make in our lifetimes is for a home. Questions that we all ask are these: How much should I spend for a particular home? How many bathrooms are there? How long...
-
Imagine a cylindrical tree of radius a. A wedge is cut from the tree by making two cuts: one in a horizontal plane P perpendicular to the axis of the cylinder and one that makes an angle u with P,...
-
Suppose R is the region bounded by y = f (x) and y = g(x) on the interval [a, b], where f(x) g(x). a. Show that if R is revolved about the vertical line x = x 0 , where x 0 < a, then by the shell...
-
What is a power curve and how is it applicable to hypothesis testing?
-
Question 2: Conversion Strategies Using Blackboard Ultra as an example, explain the following What conversion strategy was used to deploy Blackboard Ultra, the new version of Blackboard? What are the...
-
In a normal heart, which statement is true regarding the systemic and pulmonary circuits? A. Pressures are the same min both circuits B. Flow rate is the same in both circuits C. Velocity is the same...
-
Why can't the fire protection problems in a community be solved solely by building more fire stations and hiring more emergency response personnel? With fire sprinklers rated as 96% effective in...
-
21. A discrete-time signal x[n] is periodic with period 8. One period of its DFT harmonic function is {X[0],,X[7]}={3,4+ j5,-4-j3,1+ j5,-4,1- j5,-4+ j3,4-j5}. (a) What is the average value of x[n]?...
-
Discuss the role of taxonomic research in informing conservation policy and management strategies, including the identification of flagship species, the delineation of evolutionarily significant...
-
Herald Corporation, a calendar-year taxpayer, purchased and placed the following business assets in service during 2016: AssetDate Placed in ServiceInitial Cost Used computer...
-
On January 2, 20X3, Sheldon Bass, a professional engineer, moved from Calgary to Edmonton to commence employment with Acco Ltd., a large public corporation. Because of his new employment contract,...
-
If av() really is a typical value of the integrable function (x) on [a, b], then the constant function av() should have the same integral over [a, b] as . Does it? That is, does Give reasons for your...
-
a. Let a = x 0 < x 1 < x 2 < x n = b be any partition of [a, b], and let F be any antiderivative of . Show that b. Apply the Mean Value Theorem to each term to show that F(x i ) - F(x i -1 ) = (c...
-
a. Suppose the graph of a continuous function (x) rises steadily as x moves from left to right across an interval [a, b]. Let P be a partition of [a, b] into n subintervals of equal length x = (b -...
-
Combine the following and reduce to lowest terms where appropriate. a+4 2a+3 1. 5y 5y 2. 4a x - a y 47 -IX 3. + 27 - 3 MIN y z II 3X 5Y 4. 16A2B 24AB 7x 4 5. 10ab 10ab
-
Any global marketing strategy, that is in the words of Peter Drucker (2003)" any commitment of present resources to future expectations", has to start with taking stock of the changes in the global...
-
8. The graph below is a model graph for one-way bus fare for different locations A, B,C, and D. Find the four possible Hamilton circuit. the sum of the weight of the edge, and the total fare of each...
Study smarter with the SolutionInn App