(a) Show that the volume of a segment of height h of a sphere of radius r...
Question:
V = 1/3 Ïh2 (3r - h)
h
Step by Step Answer:
a V h 2 r h 3 13h 2 3r h b The smaller segment has height h 1 x and so by part a its volume is V 13 ...View the full answer
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 Calculus questions
-
Show that the volume of a general cone (Figure 20) is 5 Ah, where A is the area of the base and h is the height. Use this result to give the formula for the volume of (a) A right circular cone of...
-
Show that the volume of the vat is maximized by devoting one-third of the material to the floor and the remaining two-thirds to the walls.
-
Show that the volume of a four-dimensional ball of radius r is 2r4/2, and the volume of a five-dimensional ball of radius r is 82r5/15.
-
Write short note on context switch
-
The HR Partnership has total partners equity of $760,000, which is made up of Hall, Capital, $600,000 and Reynolds, Capital, $160,000. The partners share net incomes and losses in a ratio of 75% to...
-
Evaluate using integration by parts: f^ (x. In (5x))dx. (x In (5.x)) dx = Click here to start next step (x-In (5-x))dx = +
-
Public Expenditure on Education Figure 2.27 shows the public expenditure on education as percentage of Gross Domestic Product (GDP) for all countries. The mean expenditure is $\mu=4.7 %$ and the...
-
On January 1, 2014, Jade Company issued $2,000,000 face value, 7%, 10-year bonds at $2,147,202. This price resulted in a 6% effective-interest rate on the bonds. Jade uses the effective-interest...
-
Please solve this question with clear steps.And.Check the answers or make sure that they are right. Image transcription text 4 QUESTION 4 (40 Points) Using the finite element method, determine the...
-
You are considering a 10-year investment project. At present, the expected cash flow each year is $10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last...
-
The figure shows a horizontal line y = c intersecting the curve y = 8x - 27x3. Find the number c such that the areas of the shaded regions are equal. y= 8x-27x3
-
Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means that the rate of decrease of the volume is proportional to the area of the surface.) Show...
-
Belk Antiques uses the periodic inventory system to account for its inventory transactions. The following account titles and balances were drawn from Belks records for the year 2013: beginning...
-
Students are to select Sweden and use publicly available sources to discuss how this country's economy is performing. Use current and relevant data (at least 5 reputable sources). Use coverage of...
-
Create an executive summary that analyzes the impact that adoption of International Financial Reporting Standards would have on Swift's financial statements and its investors. For your analysis,...
-
Anna received 100 shares of Foxtrot stock as a gift from her father on November 15, Year 2, when the fair market value (FMV) of the stock was $20 per share. Her father had purchased the stock on...
-
Scott's Car Storage rents storage space for customers' cars during the winter months. The service costs $600 per car for the six-month period of October through March, with payment due up-front....
-
The Sales Growth Index (SGI) is calculated as follows: a. prior year sales divided by current year sales b. current year sales divided by prior year sales c. change in receivables divided by current...
-
In Exercises find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. y = 3 - x, y = 0, y = 2, x = 0
-
For the following exercises, write the polynomial function that models the given situation. Consider the same rectangle of the preceding problem. Squares of 2x by 2x units are cut out of each corner....
-
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 2/3v + 1, a=1
-
Find the limit. x - 9 lim >0 2 6
-
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = 3x* 5x + x? + 4, a = 2
-
To set up an optimal portfolio problem considering transactions costs, we need to adjust the expected return of stocks and calculate the transactions-cost-adjusted expected return. Suppose that a $1...
-
How to calculate the average precision (AP) for each adopted query and the mean average precision (MAP), based on both arithmetic and geometric means, must be calculated in terms of interpolated...
-
Using the relative contribution of the B to the overall expected portfolio return, show whether index leverage or single-stock leverage results in better leverage for a portfolio manager who is good...
Study smarter with the SolutionInn App