# What is Radius: Definition and 1000 Discussions

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel. The plural of radius can be either radii (from the Latin plural) or the conventional English plural radiuses. The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:

d

2
r

r
=

d
2

.

If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.
For regular polygons, the radius is the same as its circumradius. The inradius of a regular polygon is also called apothem. In graph theory, the radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph.The radius of the circle with perimeter (circumference) C is

r
=

C

2
π

.

{\displaystyle r={\frac {C}{2\pi }}.}

View More On Wikipedia.org
1. ### I Spherical trig - sphere radius from 6 lengths

Four points lie on the surface of a sphere. Given the six distances between the points, calculate the radius of the sphere. This is (allegedly) an advanced high school level problem. However, it is a remembered problem, so it is possibly misremembered (i.e. there might have been some “bice...

25. ### A Cavitation: radius of a bubble for compressible flow

The liquid-vapor mass transfer (evaporation and condensation) is governed by the vapor transport equation: $$\frac{\partial}{\partial t} (\alpha_l \rho) + \nabla \cdot (\alpha_l \rho \vec v) = \dot m^{+} + \dot m^{-}$$ In the incompressible flow case (constant density), it reduces to ...
26. ### Find the radius of the smaller circle in the tangent problem

Find the question here and the solution i.e number 10 indicated as ##6-4\sqrt{2}##, I am getting a different solution, my approach is as follows. I made use of pythagoras theorem for the three right angle triangles as follows, Let radius of the smaller circle be equal to ##c## and distance...
27. ### B Do I have enough information to find the radius?

If there is a circle, 360 degrees, and 2 random points A & B are chosen on the circle. A straight line is drawn between those two points. You are not shown the whole circle. All you can see is A, B the straight line and an arc representing an unknown number of degrees. You know the length of the...
28. ### Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg

The result is supposed to be 12,2 m but every time I get 8,016 m... I used for example this formula >r=m/[(density of air-density of hot air)*(4/3)*pi] For density I used > rho=(p*M)/(R*T) Am I forgetting something? Thanks in advance.
29. ### Why are v and a decreasing as the oribit radius increases?

I don't understand part (c) the answer is decreasing for both. I would have it decreasing for the centripetal acceleration and then increasing for the velocity, why is that not correct? Thanks in advance!
30. ### I Please check my calculation of the radius of a finite universe

My source for Ωk and H0 is https://www.cosmos.esa.int/documents/387566/387653/Planck_2018_results_L06.pdf , page 40, equation 47b. Ωk = 0.0007. Page 15 equation 13 has H0 = 67.27 km/(s Mpc). The formula I used is R = (c/H0) (1/Ωk)1/2 . ( I did have a reference for this, but I misplaced it, and I...
31. ### The radius of convergence of a series

Greetings! I have a problem with the solution of that exercice I don´t agree with it because if i choose to factorise with 6^n instead of 2^n will get 5/6 instead thank you!
32. ### Find tangential velocity given radius and the coefficient of friction

I have attempted to solve for the velocity by setting the centripetal force (mv2)/r to the normal force pointed to the center of rotation (mg). This approach seems to give the incorrect solution and I am unsure of my misunderstandings.
33. ### Bohr radius of Earth-Sun system

When I looked up for Bohr radius, the formula has ##q## in it, which is charge of the object. For this question, the electron and proton are replaced by sun and Earth so it means that I have to know the charge of Earth and sun? Thanks
34. ### Quick question about which radius to use on Gauss' law problem

confused on part A/B when I look up they did E= Q/2e(0.8)^2. But why not use the 0.100mm because that is the area of the enclosed. Same with B why did they use 100m and not 0.8m because 0.8 is smaller so it enclosed the charge
35. ### Limiting radius ratio for tetrahedral

I am able to prove that it is 0.225 but how do I prove that it is also 0.414? I need to find the max. and min. packing fraction values, which I got as a function of (r1/r2) Please help
36. ### Engineering Calculating the flux through a certain radius (concentric charged spheres)

Question My attempt for the 1st part, when r = 1.5 m Could someone confirm my answer?

38. ### Straight wire inductance vs wire radius

I know that the whole topic of inductance in a straight wire is complicated (and has led to some heated discussions in this forum :smile:). I followed Rosa's derivation and can see that it leads to an inverse relation of the inductance to the wire radius, and from what could understand, the...
39. ### Calculating magnetic field given dl, current, and radius vector

I used the above equation, and started with getting the cross product of dl and r, which was equal to 0.00195i+0.00365k. From there, I divided each component by the magnitude of radius cubed (0.827^3). I then multiplied by I and u naught(u_0=4pi*10^-7), and then divided by 4pi. The answer I got...
40. ### How Do You Calculate the Radius of a Wire Using Electrical Resistance Formulas?

i really have tried all the formulas out there and can't seem to get a solid answer
41. ### Finding the Radius of Convergence for Y=6x+16 - Troubleshooting and Solution

Greetings I have some problems finding the correct result My solution: I puted Y=6x+16 so now will try to find the raduis of convergence of Y so let's calculate the raduis criteria of convergence: We know that Y=6x+16 Conseqyently -21/6<=x<=-11/6 so the raduis must be 5/3. But this is not...
42. ### A Radius of the Sun: Can We Accurately Predict It Through Theoretical Models?

Basically, I'm wondering if there have been any attempts to calculate/model what the radius of the sun should be based on gravitational, thermal, and electromagnetic pressures. If there has, where can I find the calculation/model, and how closely does it match the actual radius of the sun...
43. ### MHB How is Radius of Curvature Computed for a Given Curve?

How did the author compute the highlighted term 2 from the highlighted term 1 in the following answer to the given question? If $\rho =\frac{d\psi}{ds}$, then the term 2 should be $\upsilon^2 \frac{d\hat{T}}{d\psi}\rho$, but instead, it was written...

50. ### Problem in finding the radius of convergence of a series

Good day I'm trying to find the radius of this serie, and here is the solution I just have problem understanding why 2^(n/2) is little o of 3^(n/3) ? many thanks in advance Best regards!