Volume of solid ring, Physics

Assignment Help:

Volume of Solid Ring

A solid sphere is bored out such that the radial axis of the removed cylinder passes through the centre. The ring of remaining material stands 6 centimetres high. What is a volume of this ring?

1359_Volume of Solid Ring.png

One way to calculate the volume of the ring is to subtract the volume of the removed material from the volume of the original sphere. This bored out material is able to be regarded as a right cylinder with spherical end caps on the two flat surfaces.

One more way is to compute the volume of the excluding the end caps, partial sphere, and then subtract the volume of the right cylinder. We will choose this method.

The volume of the partial sphere is able to be calculated by using the disk method and integrating from the top edge of the ring to the bottom edge. Using the centre of the sphere like the origin x as the horizontal axis through the centre and y the vertical axis the equation is

1824_Volume of Solid Ring1.png

The right cylinder has volume

Vc = 6πr2

= 6π(R2- 9)

Where r is the radius of the cylinder Note the requirement: R ≥ 3. So the volume of the ring is V = Vs - Vc.

Subtracting

325_Volume of Solid Ring2.png

Astoundingly this result is independent of the radius of the sphere. As long as the radius R ≥ 3 the result holds. Therefore another way to compute the volume of the ring is to compute the volume of a sphere with R = 3 representing the case of an infinitesimal bored out volume. This sphere, of course, has volume given by

V =4/3πR3= 36π


Related Discussions:- Volume of solid ring

Practical, We here at Brilliant assume that you work through these problems...

We here at Brilliant assume that you work through these problems using some sort of writing utensil. Take your pen or pencil, balance it on its tip, and let go. It falls over. How

What is the true weight of the satellite, A satellite has a mass of 5900 kg...

A satellite has a mass of 5900 kg and is in a circular orbit 3.0 x 10 5  m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 x 1

What is the characteristic of electric field graph, Regard as a Cartesian c...

Regard as a Cartesian coordinate system on which the electric potential due to an unspecified distribution of charge is a function of x only. A graph is made of V(x) vs x. The elec

Tangent galvanometer, what is the principle of tangent galvanometer?

what is the principle of tangent galvanometer?

Describe your view about piezoelectric generator, Describe your view about ...

Describe your view about piezoelectric generator. Piezoelectric generator: A slab of piezoelectric crystal is acquired and using that parallel plate capacitor is made. After

Explain newton’s law of cooling , It is described to this law, if the tempe...

It is described to this law, if the temperature T of the object is not very dissimilar from that of the environment T0, then rate of cooling -dT/dt is proportional to the temperatu

Equation of continuity, An equation that states a fluid passing through a p...

An equation that states a fluid passing through a pipe flows at a rate that is inversely proportional to the cross-sectional area of the pipe. i.e., if the pipe constricts, the flu

What are solar cells, Solar Cells: The solar cells that we see on calculat...

Solar Cells: The solar cells that we see on calculators and satellites are photovoltaic cells or modules (modules are easily a group of cells electrically  connected and packaged

What is the difference between a lens and a mirror, What is the difference ...

What is the difference between a lens and a mirror? A mirror is a reflective surface. Light passes by the glass and hits the silver backing, reflecting off of it. (The angle of

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd