A cylinder of radius r and height h has volume V = r 2 h. (a) Use

Question:

A cylinder of radius r and height h has volume V = πr²h.

(a) Use the Linear Approximation to show that

V V 2 2 r + h

(b) Estimate the percentage increase in V if r and h are each increased by 2%.

(c) The volume of a certain cylinder V is determined by measuring r and h. Which will lead to a greater error in V: a 1% error in r or a 1% error in h?

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 09:01 AM

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...
What are the units of volume? Suppose another student tells you that a cylinder of radius r and height h has volume given by r 3 h. Explain why this cannot be right.
Calculate the dollar proceeds from the FIs loan portfolio at the end of the year, the return on the FIs loan portfolio, and the net interest margin for the FI if the spot foreign exchange rate has...
When a liquid or a gas occupies a volume, it may be assumed to fill the volume completely. On the other hand, when solid particles occupy a volume, there are always spaces (voids) among the...
A cement manufacturer has supplied the following data: Tons of cement produced and sold........................................................ 267,000 Sales...
Redesign the fractionator of Example 6.8 using a random packing. The column is to be packed with 50-mm metal Pall rings. Determine the diameter of the tower, the height of packing in the stripping...
Jan Nab is the sole owner of Deer Park, a public camping ground near the Lake Mead National Recreation Area. Jan has compiled the following financial information as of December 31, 2010....
As a successful entrepreneur and CEO, you are considering making some financial decisions for your engineering company. Examining the financial report of your company, you notice: . The upgrade of...
Use the Linear Approximation to show that if I = x a y b , then 1 za- - y + b y
Let I = W/H 2 denote the BMI described in Example 6. Estimate the change in height that will decrease I by 1 if (W, H) = (25, 1.1), assuming that W remains constant. EXAMPLE 6 Body Mass Index A...
a. Use the method of Lagrangian multipliers to solve Problem 12. b. Do you get the same response as you do without using this method? c. What does equal? What does this mean?
Suppose that the magnitude of the force, P, is 39.3 N. If the mass of the spacecraft is 10,117 kg and the mass of the astronaut is 71.1 x 10 g, what is the ratio of the magnitude of the astronauts...
b. One of the steps in designing a neural network is training steps through a process called backpropagation process. To understand the backpropagation process, run the following Matlab program. clc...
In which two file types can the Ansible inventory file be represented? ( ( Choose two. ) ) INI - like XML YAML Cisco CLI
What are two MDT tools or technologies? ( ( Choose two. ) ) Pipeline SNMP show commands YANG block chain
You are configuring your Cisco ISE to support 8 0 2 . 1 8 0 2 . 1 X security for the APs in your infrastructure. You have already created the credentials that the APs will present to the wired port...
What is a financial futures contract? How does it differ from a forward exchange contract?
The area of square PQRS is 100 ft2, and A, B, C, and D are the midpoints of the sides. Find the area of square ABCD. B A
Find all the solutions, real and complex, of the equation |x 2 | = 9.
(a) Graph the circle x 2 + y 2 = 100 and the the para y = 3x 2 (b) Solve the system of equations: (c) Where do the circle and the parabola intersect? + y? = 100 %3 x?
Solve the equation 2e x = 5.
Assume that the real rate of interest is 1 . 7 3 percent and the anticipated percentage change in price levels over the life of the loan contract is 9 . 2 3 percent. What is the nominal interest rate...
Samsung has been producing the new Galaxy X250 smart phone throughout 2022 but doesn't plan to sell it until March 2023. How are these smartphones, which are sitting in a warehouse somewhere in...
Silver Water Motorworks produces small electric motors in lots of 200 with an average yield of 92%. Fifty per cent (50%) of the sub-standard output from the first run through, can be reworked. Direct...

A cylinder of radius r and height h has volume V = r 2 h. (a) Use

Question:

V V 2 2 r + h

Step by Step Answer:

Calculus

Students also viewed these Mathematics questions