The volume of a cone of radius r and height h is one-third the volume of a
Question:
The volume of a cone of radius r and height h is one-third the volume of a cylinder with the same radius and height. Does the surface area of a cone of radius r and height h equal one-third the surface area of a cylinder with the same radius and height? If not, find the correct relationship. Exclude the bases of the cone and cylinder.
Step by Step Answer:
The surface area of the de...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 the fact that the area of a circle of radius r is r2 to find the volume of a cone of height 1 that has radius r at a height r. Think of the cone as being built of a stack of little circular disks...
-
Use a double integral to find the volume of a cone of height h and radius a at the base. If the cone is standing with its point upward and with its base centered at the origin, the equation giving...
-
Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume V of the water in the cone as a function of the height...
-
A company has the following data: net sales, $405,000; cost of goods sold, $220,000; selling expenses, $90,000; general and administrative expenses, $60,000; interest expense, $4,000; and interest...
-
J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May...
-
Imagine a company offering a line of hair dryers that operate on different voltages, say, 12, 30, 60, and 120 V. Assume that all of the dryers are rated at 1,200 W and find the current that would...
-
Why is an ethical culture considered necessary for fraud prevention and deterrence?
-
Accounting for Goodwill On July 1, 2010, Brandon Corporation purchased Mills Company by paying $250,000 cash and issuing a $150,000 note payable. At July 1, 2010, the balance sheet of Mills Company...
-
4. A monopolist is faced with the inverse demand function P(Q) denoting the price when output is Q. The monopolist has a constant average cost k per unit produced. (a) Find the profit function (Q),...
-
Tuckered Outfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts, and Almonds costing, respectively,...
-
Consider the following curves on the given intervals. a. Write the integral that gives the area of the surface generated when the curve is revolved about the x-axis. b. Use a calculator or software...
-
Consider the upper half of the astroid described by x 2/3 + y 2/3 = a 2/3 , where a > 0 and |x| a. Find the area of the surface generated when this curve is revolved about the x-axis. Use symmetry....
-
Two points, A and B, are on an isoquant drawn with labor on the horizontal axis and capital on the vertical axis. The capital-labor ratio at B is twice that at A, and the elasticity of substitution...
-
After listening to the lecture on online presentations, please comment with at least two complete sentences for each of the items listed below on how you plan to manage them in an online speech. The...
-
1. A reaction to the podcasts, particularly "How to Cover, Political Diversity in America"? Do you agree with the information? 2. How do you view the coverage of politics in America or where you live?
-
Now that you have learned more about health career planning, are you still interested in pursuing it yourself? Why? Write your answers on a separate sheet of paper.
-
1. From the "Eight Facts About Immigrants and Immigration" article, identify a fact that surprised you. Why were you surprised? Has your thinking changed since reading the article? If so, how? If...
-
How much are your choices of products, services, and even lifestyles and values affected by advertising? Consider the clothes you wear, the coffee you drink, the car you drive, even the neighbourhood...
-
Explain why financial markets may be less liquid if companies are not forced to provide accurate financial reports.
-
State whether each statement is true or false. If false, give a reason. {purple, green, yellow} = {green, pink, yellow}
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If {a n } and {b n } are divergent, then {a...
-
List the first five terms of the sequence. aj = 6, an+1 = an n
-
Test the series for convergence or divergence. 00 n=1 20 n (1 + n)3"
-
What are the structural and functional adaptations of photosynthetic pigments, such as chlorophylls and carotenoids, and how do they optimize light absorption, energy transfer, and photoprotection in...
-
An analyst gathered the following information for a stock and market parameters: stock beta = 1.5; expected return on the Market = 9.4%; expected return on T-bills = 0.61%; and current stock Price =...
-
You have $55,000 in your retirement account that is earning 4% per year. How many dollars in withdrawals per year would reduce this nest egg to zero in 20 years?
Study smarter with the SolutionInn App