Let V be the volume of a can of radius r and height h, and let S

Question:

Let V be the volume of a can of radius r and height h, and let S be its surface area (including the top and bottom).

Find r and h that minimize S subject to the constraint V = 54π.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 16, 2024 09:02 AM

See More Questions

The shape of a bacterium can be approximated by a cylinder of radius r and height h capped on each end by a hemisphere. The volume and surface area of the bacterium are given by It is known that the...
In Exercises 52 through 56, you need to know that a cylinder of radius r and height h has volume V = r 2 h and lateral (side) surface area S = 2rh. A circular disk of radius r has area A = r 2 . A...
In Exercises 52 through 56, you need to know that a cylinder of radius r and height h has volume V = r 2 h and lateral (side) surface area S = 2rh. A circular disk of radius r has area A = r 2 . A...
Millennium Textiles Company makes silk banners and uses the weighted-average method of process costing. Direct materials are added at the beginning of the process, and conversion costs are added...
The chemical reactor shown below has a cover (called a head) that is held in place by a series of bolts. The head is made of stainless steel (SG = 8.0), is 3 in. thick, has a diameter of 24 in., and...
On five-cycle semi-logarithmic paper, plot the grain-size distribution curves from the following mechanical analysis data on six soils, A through F. For each soil determine the effective size as well...
Quilts R Us (QRU) is considering investing in a new patterning attachment with the cash flow profile shown in the table below. QRU's MARR is 13.5 percent/year. a. What is the internal rate of return...
Professor Patricia (Patty) Pate is retired from the Palm Springs Culinary Arts Academy (PSCAA). She is a single taxpayer and is 68 years old. Patty lives at 98 Colander Street, Henderson, NV 89052....
Sales for a new car is expected to grow according to the equation: S = 150000(1-e -0.06t ), where t = months i) Calculate the number of cars sold after one year. ii) Calculate the number of cars sold...
Show that for both of the following two problems, P = (r, h) is a Lagrange critical point if h = 2r: Minimize surface area S for fixed volume V. Maximize volume V for fixed surface area S . Then...
In a contest, a runner starting at A must touch a point P along a river and then run to B in the shortest time possible (Figure 17). The runner should choose the point P that minimizes the total...
Consider the network shown below, and assume that each node initially knows the costs to each of its neighbors. Consider the distance-vector algorithm and show the distance table entries at node z. 1...
?What is bagging in the context of random forests Boosting the performance of individual trees Combining predictions from multiple trees Reducing the number of features .CO Pruning the branches of...
is a branch of computer science that focuses on creating computer systems or computer-controlled machines that have an ability to perform tasks usually associated with human intelligence. Natural...
2) Al systems that help people discover things they may like but are unlikely to discover on their own are known as recommendation engines. crowdsourcing systems. intelligent personal assistants....
Which of these is a super class of all errors and exceptions in the Java language? O a . . None of the above O b . . Catchable O c . . RunTimeExceptions O d . . Throwable
In what order does Prim's algorithm add edges to the MST? Whenever there is a choice of nodes, choose the one that comes alphabetically first. Whenever there is a choice of edges, choose the one with...
What do current, historical, and average exchange rates mean in the context of foreign currency translation? Which of these rates give rise to translation gains and losses? Which do not?
Draw the appropriate control flow graph of the given pseudocode.Make sure to only use one number for blocks of code which are all sequential and when the first line is executed, all of those lines...
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = 1 x
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = x 1 || x-1
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = |2x| x-3
Let X Unif(1, 2) and let Y = X. 2 a) Use the delta method to approximate the mean and variance of Y. b) Compute the exact values of E(Y) and Var(Y). c) Which approximations are better, the ones in...
Can you elucidate the complex life cycles and ecological roles of protists in various ecosystems, including their contributions to primary production, nutrient cycling, and symbiotic interactions...
What is "substantive due process"? What is the equal protection of the law?

Let V be the volume of a can of radius r and height h, and let S

Question:

Step by Step Answer:

The volume of the can is Vrh rh and its surface area is S rh 2r 2rh We want to minimize S ...View the full answer

Calculus

Students also viewed these Mathematics questions