The surface area S of a sphere of radius r feet is S = S(r) = 4r
Question:
The surface area S of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 2.
Step by Step Answer:
Sr 4r at r 2 SrS 2 r2 S2 lim r2 lim r2 lim ...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
-
Express each statement as an equation involving the indicated variables. The surface area S of a sphere is 4 times times the square of the radius p r.
-
Find the volume V and surface area S of a sphere of radius 4 centimeters.
-
Find the volume V and surface area S of a sphere of radius 3 feet.
-
Write a program that takes as command-line arguments the name of an image file and the pixel coordinates of a rectangle within the image; reads from standard input a list of Color values (represented...
-
On February 15, 2016, Rooker, Madras & Associates compiled the following information concerning inventory for five years. It used the dollar-value LIFO retail inventory method. Compute the inventory...
-
The theoretical information ratio of a portfolio P is defined as where RP is the portfolio return, and RMP is the return on the market portfolio. Show that this ratio can never be larger than the...
-
1. Identify an entrepreneur in your area you would like to interview. 2. Contact the person you have selected and make an appointment. Be sure to explain why you want the appointment and to give a...
-
Garcia Home Improvement Company installs replacement siding, windows, and louvered glass doors for single-family homes and condominium complexes in northern New Jersey and southern New York. The...
-
3. If the policy proposed in question 2 is adopted, analyze the potential effects of this policy on the demand for workers under the age of 65. That is, if employers who want their employees to be...
-
There is an array A made of N integers. Your task is to choose as many integers from A as possible so that, when they are put in ascending order, all of the differences between all pairs of...
-
The volume V of a right circular cylinder of height 3 feet and radius r feet is V = V(r) = 3r 2 . Find the instantaneous rate of change of the volume with respect to the radius r at r = 3.
-
The volume V of a sphere of radius r feet is V = V(r) = 43r 3 Find the instantaneous rate of change of the volume with respect to the radius r at r = 2.
-
How does the performance of non-restoring and nonperforming division compare? Demonstrate by showing the number of steps necessary to calculate A divided by B using each method. Assume A and B are...
-
Consider the following interface: interface Something { boolean validate (int value); Classes that implement "Something" interface can validate a specific value in different behaviors within some...
-
explain how to implement a restaurant menu that has a scrollable first main page and is also clickable using JAVA in Android Studio? I just need an example for one food item to grasp the logic behind...
-
From the Disney financial records provided below,construct the company's balance sheet: Machine and Equipment $450,000. Inventories are $253,125. Cash in the coffer (cash box) $26,000 and cash in the...
-
1. What specific suggestions would you make in terms of sales call allocation strategy for Brenda to make better use of available selling time in calling on these new accounts?
-
Solve detailly on excel with formulas UIBS SR United International Business Schools EUROPEAN college for liberal studies WORKING CAPITAL MANAGEMENT GROUP ASSIGNMENT For this Group Assignment, worth...
-
Explain the term reciprocal services and give examples of the reciprocal services offered by support departments in a university.
-
A manufacturer can sell product 1 at a profit of $20 per unit and product 2 at a profit of $40 per unit. Three units of raw material are needed to manufacture one unit of product 1, and six units of...
-
In Problems 7586, perform the indicated operations and simplify the result. Leave your answer in factored form. x 2 x + 1 x x-2 x + 3
-
In Problems 67 90, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 3y)(x - 3y)
-
Make up a radical equation that has no solution.
-
Use the following data to calculate the cost of ending inventory using the l I f o method. September 1 st beginning inventory 1 5 units at $ 2 0 Each. September 1 0 th purchase 2 0 units at $ 2 5...
-
Dunder Mifflin started the month of June with $ 1 2 2 , 8 8 9 in assets. During the month of June, they bought $ 7 0 , 0 6 4 worth of paper on account and received $ 2 4 , 7 4 1 from a customer on...
-
Discuss at least two legal implications or ethical issues in creating a training course that discusses culture. Identify what laws and regulations should be considered. Explain how the demographic...
Study smarter with the SolutionInn App