For a cylinder with radius r and height 3r. For each of the given shapes, find the
Question:
For each of the given shapes, find the constant c in the power relationship S = cV2/3 between the surface area S and volume V. By how much is does c exceed the value (36π)1/3 = 4.836 for the sphere (which is in fact the minimum for any shape).
Step by Step Answer:
The cylinder has surface area S 2r 2 6r 2 8r 2 The volume ...View the full answer
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler
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
-
When gas expands in a cylinder with radius r, the pressure at any given time is a function of the volume: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the...
-
Solve each problem The volume of a right circular cylinder is jointly proportional to the square of the radius of the circular base and to the height. If the volume is 300 cm 3 when the height is...
-
Several mathematical stories originated with the second wedding of the mathematician and astronomer Johannes Kepler. Here is one: While shopping for wine for his wedding, Kepler noticed that the...
-
rn Explain in some detail how the Precision Tree calculations in Figure 6.11 for the Acme problem are exactly the same as those for the hand-drawn decision tree in Figure 6.6. In other words, explain...
-
From 1991 to 2000, the U.S. economy had an annual inflation rate of around 2.93%. The historical annual nominal risk-free rate for this same period was around 5.02%. What is the real interest rate...
-
Octane (C8H18) is burned with dry air. The volumetric analysis of the products on a dry basis is 9.21 percent CO2, 0.61 percent CO, 7.06 percent O2, and 83.12 percent N2. Determine (a) The airfuel...
-
We see that 75 of the 264 people in the study allowed the pressure to reach its maximum level of \(300 \mathrm{mmHg}\), without ever saying that the pain was too much (MaxPressure=yes). Use this...
-
Your firm has been engaged to do the current years audit of Dawood Ltd., a medium sized business involved in manufacturing television screens and monitors. Dawood is privately owned and its two...
-
Thornton Enterprises produces a product with fixed costs of $37,600 and variable cost of $3.30 per unit. The company desires to earn a $24,000 profit and believes it can sell 11,000 units of the...
-
1. Weekend breaks sell for 300 each. Ten per cent is payable when the holiday is booked and the remainder after two months. 2. Travel agents are paid a commission of 10 per cent of the price of the...
-
For a cube with side length w. For each of the given shapes, find the constant c in the power relationship S = cV2/3 between the surface area S and volume V. By how much is does c exceed the value...
-
The -3/2 law of self-thinning in plants argues that the mean weight W of surviving trees in a stand increases while their number N decreases, related by W = cN-3/2. Suppose 104 trees start out with...
-
Rationalize the numerators in Problem. Vi - V 2 - x?
-
A bank pays a floating rate of interest on deposits (i.e. liabilities) and earns a fixed rate of interest on loans (i.e. assets). This mismatch between assets and liabilities can cause tremendous...
-
Suppose the estimated logit model is Z=6.165.36X - 3.14X2 + error where X, is cash flow to debt ratio and X2 is current assets to current liability Borrower Borrower A Borrower B 0.14 0.38 X2 2.55...
-
Janet buys a one-year put and a one-year call on a share of XYZ stock according to the following information: option put call strike price $55 $55 option premium $4.13 $6.75 XYZ does not pay any...
-
Explain 4 factors that can influence the supply and demand of loanable funds which are responsible for the variation of the risk-free rates across countries
-
If a firm is using cash or reinvesting in itself, would they use the current federal interest rate plus a theoretical premium or would they use their current rate on existing debt? How would a firm...
-
Refer to the data in Solved Problem F.1 which deals with Higgins Plumbing and Heating. Higgins has now collected 100 weeks of data and finds the following distribution for sales: a) Assuming that...
-
An example of prescriptive analytics is when an action is recommended based on previously observed actions. For example, an analysis might help determine procedures to follow when new accounts are...
-
Let C(x) = 5x + 250 and R(x) = 27x. (a) Write the profit function P(x). (b) What is the slope of the profit function? (c) What is the marginal profit? (d) Interpret the marginal profit?
-
Solve the equations in Problems. 1. 3x - 8 = 23 2. 2x - 8 = 3x + 5 3. 4. + 3 5( 2) 6. 2x +-=-+ 2 2 3
-
1. If p = 3q3, is p a function of q? 2. If y2 = 9x, is y a function of x? 3. If R = 3(x + 4, is R a function of x? 4. What are the domain and range of the function y = (9 - x?
-
(a) Approximate the following transfer function by removing a non-dominant pole (or a pair of non-dominant poles): (2 Marks) G(s) = = 0.2(s + 2) (s+ 0.5)(s+3 0.8j) (b) Is the following a valid state...
-
(a) Given that z =2+23i and z =-5+5i. Express, and in polar form. (b) Find z and in exponential form. (c) Find (5)*() in the forms of x+yi.
-
Evaluate the impact of mobile banking on traditional revenue streams and business models of banks, such as transaction fees, interchange fees, and overdraft charges. How do banks monetize mobile...
Study smarter with the SolutionInn App