EXAMPLE 4The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is themaximum error in using this value of the radius to compute the volume of the sphere?SOLUTIONIf the radius of the sphere is r then its volume is V =If the error in the measured value of r is denoted by dr = Ar, then thecorresponding error in the calculated value of V is AV, which can be approximated by the differentialdV = 4rrdr.When r = 23 and dr = 0.02, this becomesdV =4x((round to the nearest integer).The maximum error in the calculated volume is aboutcm3.

Given: Radius of sphere =23 cm Error in radius = dr = 0.02 Volume of sphere = V=43πr3

EXAMPLE 4 The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere? SOLUTION If the radius of the sphere is r then its volume is V = ar. If the error in the measured value of r is denoted by dr = Ar, then the %3D corresponding error in the calculated value of V is AV, which can be approximated by the differential dV = 4xr dr. When r= 23 and dr = 0.02, this becomes dV = 4x( (round to the nearest integer). The maximum error in the calculated volume is about cm3.

EXAMPLE 4 The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere? SOLUTION If the radius of the sphere is r then its volume is V = ar. If the error in the measured value of r is denoted by dr = Ar, then the %3D corresponding error in the calculated value of V is AV, which can be approximated by the differential dV = 4xr dr. When r= 23 and dr = 0.02, this becomes dV = 4x( (round to the nearest integer). The maximum error in the calculated volume is about cm3.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: calculating the volume of the sphere

A: Given: A radius of a sphere is to be 3 cm with a possible error of 0.02 cm. Where, r=3 cm and…

Q: A rectangular waterbed is 6 ft long, 3 ft wide, and 1 ft tall. How many gallons of water are needed…

Q: Datal [year] # of pennies volume of pennies 11987 54 2018 53 Ave voll Ave density 7.508 g/mL…

A: Given information: The data for the year, average volume, and average density are given.

Q: The question is asking for CM/min. Are you sure this is the solution to

Q: If each of the dimensions of a rectangular box is measured with an error not exceeding 1%, what i…

Q: A rectangular sheet of metal of length=30cm and width = 28cm has a square of side x cm cut from each…

Q: You are given the following information: äx:T0j = 7.6491 Ax+1:9| = 6.59609 Ax+2:5| = 6.00768 i =…

A: Given: i = 0.05 a¨x:10=7.6491ax+1:9=6.59609ax+2:8=6.00768

Q: (7) The radius of a sphere was measured and found to be 20 cm with a possible error in measurement…

A: Given: Radius (r) = 20 cm ∆r = ±0.05 cm

Q: A rectangular box which is open at the top can be made from an 6-by-30-inch piece of metal by…

A: A rectangular box which is open at the top can be made from an width 6inch and length30Inch piece of…

Q: the for the dia and n 8.3 101 the he ight-chcular cyinder is puted using the values a Use the Linear…

Q: Show that if MG, NAG and NM, then (G/N)/(M/N) ≈ G/M.

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Here we will find the amount of paint required,

Q: . Order: Colace Syrup 20 mL Label: Colace Syrup (docusate sodium) 20 mg per tsp (teaspoon) Use…

A: Answer: Dose ordered = 20 ml Dose in hand = 20 mg per tsp This means ----1 tsp = 100/20= 5ml So to…

Q: Surface Area & Volume Calculate the surface area of this shape: cm² 5.5 cm 5.5 cm BE H

A: Surface Area of a cuboid whose dimensions are ( l , b , h ) is given as A = 2( lb + bh + hl ) Given…

Q: E determine µ when z =\2.5, x = 42.1 and o = 2 %3D %3D

A: Topic:- algebra

Q: 60) Find the values of h for which y= e satısfics the equation yty'= y".

Q: The volume of a solid can be expressed as V=7x3. The volume is to be calculated with an error of no…

A: To find: Approximately the greatest error that can be tolerated in the measurement of x. Given…

Q: If x> 0, y>0 and x-y =2xy, find the exact value of y -

A: If x>0, y>0 and x2-y2=2xy, then to find the exact value of xy.

Q: Body Mass Index (BMI) is a measurement of a person's weight with respect to his or her height. BMI…

A: Given the data as Weight W pounds BMI B 115 20 149 24 108 20 160 30 127 25 123 21…

Q: Find a formula for the described function and state its domain Express the surface area of a cube as…

A: Consider the provided expression, Let V be the volume of the cube with length side a. V=a3 So, the…

Q: An open-top box is to be made from a 18-inch by 36-inch piece of plastic by removing a square from…

A: Given : An open-top box is to be made from a 18-inch by 36-inch piece of plastic by removing a…

Q: Can balloons hold more air or more water before bursting? A student purchased a large bag of 12-inch…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

EXAMPLE 4
The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the
maximum error in using this value of the radius to compute the volume of the sphere?
SOLUTION
If the radius of the sphere is r then its volume is V =
If the error in the measured value of r is denoted by dr = Ar, then the
corresponding error in the calculated value of V is AV, which can be approximated by the differential
dV = 4rr
dr.
When r = 23 and dr = 0.02, this becomes
dV =
4x(
(round to the nearest integer).
The maximum error in the calculated volume is about
cm3.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

One mole of an ideal gas will occupy 22.414 L of volume at one atmosphere of pressure and a temperature of 273.15 K. O True O False
3. y = In? (csc2x). Find y" у %3D
3 The mass of a uniform sphere varies directly with the cube of its radius. A certain sphere has radius 3cm and mass 113.1 g. Find the mass of another sphere with radius 5 cm.
: Ebobl solve the initiat Valu problem %3esince-2) y(an2)=0
A box with square base and height t is measured with the same possible error of measurement. Calculate the maximum possible error for its surface area if the length is 2 cm and the height is 6 cm and the percentage error of volume must be kept within +1%. (c)
H.W. 1) Calculate the volume of cylinder has 15 m height and 8 m diameter. 2) If we have other cylinder with the same height but it volume greater than first cylinder by 20%, how long its radius? 3) Write a program to calculate the volumetric and mass flow rate of a liquid flowing in a pipe with a velocity equal to 0.5 m/s. Knowing that the diameter of this pipe is 0.1 m and the density of this liquid is 890 kg/m³ ? 4) For the following distillation column write a code to find the value of stream B and the compositions of stream D? D=80 X% ? S%? T%? Z% ? F=100kg 15% X 25% S 40% T 20% Z B=? 15% X 25% S 40% T 20% Z 9 5) Compute the reaction rate constant for a first-order reaction given by the -E/RT Arrhenius law k = A e at a temperature T = 500 K. Here the activation energy is E=20 kcal/mol and the pre-exponential factor is A=10¹3 s¹. The ideal gas constant is R=1.987 cal/mol K.
The k-value for a gas is 1.2. What is the volume of the gas in terms of the pressure it exerts? OV = 1.2 P OV= 1.2 – P OV = oV=