The lateral surface area of a cone of radius r and height h (the surface area excluding
Question:
The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r2 + h2.
a. Find dr/dh for a cone with a lateral surface area of A = 1500π.
b. Evaluate this derivative when r = 30 and h = 40.
Step by Step Answer:
So rr 2 h 2 r 2 r r...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
-
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...
-
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...
-
If the surface of a cone of slant height C and base radius r is cut along a lateral edge and laid flat, it becomes the sector of a circle of radius C and central angle θ (see Figure 19)....
-
You want to short a 6-month forward contract on a stock. You contacted your bank and were offered a forward price of $39.85 [Note: This forward price is available only to customers who want to take a...
-
S. Bullock, a farmer, makes up his financial statements to 31 March each year. The trial balance extracted from his books as at 31 March 20X3 was as follows: On 31 March 20X3: Included in the...
-
Morton Corp., a calendar-year C corporation, started business in Year 1. In Year 5, the company sold its office building and office furniture, and purchased a new office building and office...
-
The commercial refrigerating machine follows the principle of the (a) Carnot cycle (b) Reversed Carnot cycle (c) Stirling cycle (d) None of these.
-
The July 1, 20X5, trial balance for the Bond Redemption and Interest Debt Service Fund of the County of Hawaii, Hawaii, is presented here. The resources of the fund are committed to debt service. The...
-
The overall cost of the implementation might dictate how the organization approaches the installation. Some organizations hire temporary staff to fill certain roles. Is there a downside to hiring...
-
Consider two different machines, with two different instruction sets, both of which have a clock rate of 200 MHz. The following measurements are recorded on the two machines running a given set of...
-
Find the derivative of the following functions. y = f(x)g(x), where f and g are differentiable and non negative at x.
-
Prove the following identities and give the values of x for which they are true. cos (2 sin -1 x) = 1 - 2x 2
-
Change from rectangular to cylindrical coordinates. (a) (-1, 1, 1) (b) (-2, 23 , 3)
-
Larry Riley formed a rental agreement for a self-storage unit with Iron Gate Self Storage in December 2003. The agreement stated that a maximum of \($5,000\) of personal property could be stored in...
-
What are the different types of schemes associated with complex frauds?
-
When the plaintiff was 16, he was employed by Kmart as a cashier. At the end of his training, he was required to read Kmarts policy agreement, which included an agreement to submit all employment...
-
What are some indicators that a digital device has been infected?
-
Parents of minors took Apple to court in 2012 for supplying game applications, on iPhones, that were free but through which users could purchase in-game currencies. Apparently, parents would log on...
-
Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress,...
-
To help you become familiar with the accounting standards, this case is designed to take you to the FASBs Web site and have you access various publications. Access the FASBs Web site at...
-
Find the volume of the solid that lies under the plane 4x + 6y - 2z + 15 = 0 and above the rectangle R= {(x, y) | 1
-
Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y 2 - x 2 + 2 and above the rectangle R = [-1, 1] x [1, 2].
-
Find the volume of the solid lying under the elliptic paraboloid x 2 y 4 + y 2 /9 + z = 1 and above the rectangle R = [-1, 1] x [-2, 2].
-
An eagle is flying horizontally at a speed of 2.9 m/s when the fish in her talons wiggles loose and falls into the lake 4.4 m below. Calculate the magnitude of the velocity of the fish relative to...
-
Because of its high dielectric strength, SF6 (sulfur hexafluo-ride) gas is widely used as an insulator and a dielectric in HV applications such as HV transform-ers, switches, circuit breakers,...
-
Roberta Bondar is travelling in her space craft around a distant planet. The planet has a radius R' and she is at an altitude of 2R' above its surface, coasting at some constant speed in a circular...
Study smarter with the SolutionInn App