For the can problem in Example 4, the minimum surface area required that the height be twice
Question:
For the can problem in Example 4, the minimum surface area required that the height be twice the radius. Show that this is true for a can of arbitrary volume V.
Example 4
A coffee company wants to manufacture cylindrical aluminum coffee cans with a volume of 1000 cm3 (1 liter). What should the radius and height of the can be to minimize the amount of aluminum used?
Step by Step Answer:
Treat V as ...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 Mathematics questions
-
What can we say is true as a result of people engaging in voluntary trade? A. One person gains and the other loses. B. One person gains while there is a neutral effect on the other person. C. Both...
-
A cylindrical glass of radius and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base. (a) Determine a way to slice the water into parallel...
-
A block of aluminum with a volume of 10 cm3 is placed in a beaker of water filled to the brim. Water overflows. The same is done in another beaker with a 10-cm3 block of lead. Does the lead displace...
-
Include another public method in the Employee class from Pencil and Paper Exercise 3. The method should calculate an Employee objects new salary, which is based on the raise percentage provided by...
-
Refer to the information for Billings Company above. Billings Company produces two products, Product Reno and Product Tahoe. Each product goes through its own assembly and finishing departments....
-
Find the derivative of the function. F(x) *2x arctan t dt
-
For each of the following, decide whether there has been a valid offer: A . Would you like to buy my cabin in Maine? Its a beautiful piece of lakefront property and could sell for more than...
-
After spending $3 million on research, Better Mousetraps has developed a new trap. The project requires an initial investment in plant and equipment of $6 million. This investment will be depreciated...
-
11 12 13 14 Height of a plant is regulated by: a) DNA which is directly influenced by growth hormone. b) Genes which regulate the proteins directly. Growth hormones under the influence of the enzymes...
-
A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 2 ft per...
-
Suppose the demand for tickets to an amusement park can be estimated by the function D(p) = -25p 2 + 63,075, where p is the price for one ticket. (a) Find the elasticity of demand E. (b) If the price...
-
In 2015, Amanda and Jaxon Stuart have a daughter who is one year old. The Stuarts are full-time students and they are both 23 years old. Their only sources of income are gains from stock they held...
-
On August 1, 2015, Lifters, a gym, sells 5 annual memberships for $1,500 each. What would the entry look like to record the receipt of cash as deferred revenue?
-
enjamin and Nellie Barker have taxable income of $120,000. Several of the items used to calculate their taxable income included W-2 wages of $150,000, and Net Long-Term Capital Losses of $6,000....
-
Differentiate and describe the different types of budgets commonly used by the healthcare facilities ( be sure to label the responses with appropriate numbers) compare incremental budgeting and zero...
-
Your GST bill has arrived. You need to pay GST on $153,890. How much do you need to pay in GST? Explain.
-
Is there accountability for Federal Government spending? If you believe there is accountability, please discuss briefly the nature of that accountability ?
-
Sam Walton (Walmart), Debbi Fields (Mrs. Fields [cookies]), and Sean Combs (Sean John [clothing]) are some well-known successful entrepreneurs. What common traits do these individuals possess that...
-
In 1995 Miguel purchased a home for $130,000. In 2000 he sold it for $170,000 and immediately purchased another one for $180,000, which he sold in 2007 for $235,000. How much taxable capital gain, if...
-
Classify each of the functions in Exercises 6370 as even, odd, or neither. f(x) = x/(x 2 - 9)
-
Classify each of the functions in Exercises 6370 as even, odd, or neither. f(x) = 1/(x 2 +4)
-
Solve each equation in Exercises 4164. Round decimal answers to four decimal places. 5(0.10) x = 4(0.12) x
-
3. Decompose the rational expression into a sum of partial fractions. 2x+1 x(x+1)
-
Let U = {1, 2, 3, ..., 5600}. Let S be the subset of the numbers in U that are multiples of 8, and let T be the subset of U that are multiples of 3. Since 5600-8 = 700, it follows that n(S)= n({8.1,...
-
Problem 6(*): Let f : [2,6] R be the function defined by f(x)=-1 2 if 2x <3 if 3x <5 3 if 5 x 6. For >0, find a partition P of [2,6] such that U(f, P) - L(f, P) < .
Study smarter with the SolutionInn App