Question

In: Math

You plan to calculate the volume of a tall, thin cylinder from measurements of its radius...

You plan to calculate the volume of a tall, thin cylinder from measurements of its radius and height. Which dimension should you measure more carefully? Give reasons for your answer.

Expert Solution

The volume of the cylinder with radius "r" and height "h" is given by

If the error in height is then

Similarly if the error in radius be

Then the error in its volume

Since the product of are smal we can ignore them

Dividing both sids by

Hence the maximum relative error in volume

As we can see the relative error in radius contribute more to relative error in volume

So radius of the wire is to be measured more accurately to minimize the error in Volume.

milcah answered 3 years ago

) A coaxial cable consists of a cylinder of radius ? surrounding by a thin cylindrical...

) A coaxial cable consists of a cylinder of radius ? surrounding by a thin cylindrical shell of radius 2?. Suppose the cable is along the ?-axis. The current density in inner cylinder is ? ⃗= (?0 + ??)?̂, where ?0 > 0 and ? > 0 are constant. The current in the outer shell, ?? ,is downward (−? direction). a) Find the magnetic field in regions 0 < ? < ?,? < ? < 2? and 2? < ?....

There is an elongated metal cylinder with a thin, hollow radius of R. The net propagation...

There is an elongated metal cylinder with a thin, hollow radius of R. The net propagation density is 2λ. An infinitely long conductor with a propagation density of λ lies along the central axis of the cylinder. When λ is positive, find the electric field strength at (a) the inner r <R of the cylinder, and (b) the outer r> R of the cylinder. (c) Determine the direction of the electric field for each. (Draw a picture and explain it)

Write a program that reads in the radius and length of a cylinder and computes volume...

Write a program that reads in the radius and length of a cylinder and computes volume using the following formulas: area = radius * radius * PI volume = area * length

The volume of a right circular cylinder with base radius ? and height ℎ is given...

The volume of a right circular cylinder with base radius ? and height ℎ is given by: ? = ??^2ℎ. If the base radius is decreasing at a rate of 3 inches per minute and the height is increasing at a rate of 2 inches per minute, at what rate is the volume of the cylinder changing when the radius is 8 inches and the height is 3 inches. Will the volume be increasing or decreasing at this instant? Be...

a. Calculate the approximate volume of the tall feature in cubic meters. The top of the...

a. Calculate the approximate volume of the tall feature in cubic meters. The top of the feature is at an elevation of 115’ and the bottom of the feature is at an elevation of 35’. The width of the feature is 1410’ and its length is 1245’. Show your work clearly. b. Do you think this calculated volume is an overestimate or underestimate? Explain your reasoning

A thin-walled hollow cylinder with mass m1 and radius R1 rolls without slipping on the inner...

A thin-walled hollow cylinder with mass m1 and radius R1 rolls without slipping on the inner wall of a larger thin-walled hollow cylinder with mass m2 and radius R2 >> R1. Both cylinders' axes are aligned and horizontal, and some magical mechanism ensures this perfect friction contact between them. Unfortunately for you, the larger cylinder rolls without slipping on a horizontal surface. Describe the motion including small oscillation frequencies near any equilibria if the systems is released from rest with...

An infinitely long right circular cylinder has radius ?. There is a non-constant cylindrically symmetric volume...

An infinitely long right circular cylinder has radius ?. There is a non-constant cylindrically symmetric volume charge density ?(?), where ? is the (radial) distance from the axis of the cylinder, given by ?(?) = ((?0*?)/?)sin((2??)/?), where ?0 is a constant. 1. Consider a concentric cylinder with radius ? and length ?. Compute the total charge ?(?) inside the cylinder for 0 < ? < ? and for ? > ?. 2. Go back to the infinite cylinder setup and...

If a hoop and a cylinder of the same mass and radius are realeased from rest...

If a hoop and a cylinder of the same mass and radius are realeased from rest at the top of an incline at the same time, which one will reach the bottom first?

How do I calculate the volume of a cylinder if the surface of the cylinder is 4239 cm². And the height is equal to the diameter of the base.

An infinitely long solid insulating cylinder of radius a = 2.1cm is positioned with its...

An infinitely long solid insulating cylinder of radius a = 2.1 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 27μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.9 cm, and outer radius c = 17.9 cm. The conducting shell has a linear charge density λ = -0.36μC/m.1 What is Ey(R), the y-component of the electric field at point...