Determine radius of sphere from volume?

Question

I can't seem to solve the age old sphere volume equation (V=(4/3)*PI*r^3) for volume. This is driving me crazy so please help me out if you get a chance!

Sorry - typo - I'm trying to solve for the Radius - I have the volume.

Thanks for the correct formula! I used it in Actionscript (Flash) to do this:
http://www.teratechnologies.net/devel/spheres.html

In case somone else wants to add 2 spheres in Actionscript and get the redius of the resulting sphere, here's the code:

Radius = Math.pow(volume/((4/3)*Math.PI),(1/3))

Answer 1

You basically need to get r by itself.

V = (4/3)* PI * r^3 ---> divide both sides by 4/3 and PI
V/[(4/3)* PI] = r^3 ---> Take cube root on both sides
{V/[(4/3)* PI] }^(1/3) = r

Answer 2

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The easiest way to figure this out is to take a cross-section of the sphere. This will give you a circle with the same radius of the sphere. Now, the cross-section of a cone is a triangle, so the trick is to find the largest triangle that can be inscribed in a circle. r = 20 A = (1/2) * b * h h = 20 + k (where k is some distance below the center of the circle b = 2 * sqrt(20^2 - k^2) (if you draw this diagram out, you'll see that the angle made by the height of the triangle and the base of the triangle will be a right angle, so we can use Pythagorean's theorem to solve for b in terms of k) A = (1/2) * (20 + k) * 2 * sqrt(20^2 - k^2) A = (20 + k) * sqrt(400 - k^2) I don't know if you're in calculus, but I'm going to cheat a bit. I'm going to take the derivative of A with respect to k and set that to 0 in order to solve for k dA/dk = (20 + k) * (1/2) * (-2k) / sqrt(400 - k^2) + sqrt(400 - k^2) * 1 dA/dk = 0 0 = (20 + k) * (-k) / sqrt(400 - k^2) + sqrt(400 - k^2) (20 + k) * k / sqrt(400 - k^2) = sqrt(400 - k^2) (20k + k^2) = 400 - k^2 20k + k^2 = 400 - k^2 2k^2 + 20k - 400 = 0 k^2 + 10k - 200 = 0 k = (-10 +/- sqrt(100 + 800)) / 2 k = (-10 +/- sqrt(900)) / 2 k = (-10 +/- 30) / 2 k = -5 +/- 15 k = -20 , 10 k = 10 b = 2 * sqrt(400 - 100) => 2 * sqrt(300) => 2 * 10 * sqrt(3) = 20 * sqrt(3) h = 20 + 10 = 30 (you should note that this makes an equilateral triangle. Remember that the largest triangle you can inscribe in a circle is an equilateral triangle) Now, let b serve as the base of the cone. The radius of the base will be 10 * sqrt(3) cm. The height will be 30 cm. The rest is plug and play V = (1/3) * pi * r^2 * h V = (1/3) * pi * (10 * sqrt(3))^2 * 30 V = 10 * pi * 100 * 3 V = 3000 * pi 3000 * pi cm^3

Answer 3

Radius Of Sphere

Answer 4

This Site Might Help You.

RE:
Determine radius of sphere from volume?
I can't seem to solve the age old sphere volume equation (V=(4/3)*PI*r^3) for volume. This is driving me crazy so please help me out if you get a chance!

Answer 5

We can use integration to find the volumes of a variety of geometric solids. On this page, we will apply this idea to some particularly simple examples, the sphere and the hyperboloid. The nice property of these is that they are symmetric about some axis of rotation. Indeed, we can describe the surfaces that enclose these shapes by a single curve (the "profile") which is rotated about an axis. We call these shapes surfaces of revolution, and as will be evident below, computing the enclosed volume is a simple procedure involving integration.

Answer 6

Volume of a spere formula

v = 4/3 πr³

Answer 7

V = 4/3 * Pi * r^3

V*3/4 = Pi * r^3

3/4 * V/Pi = r^3

CubeRoot(3/4 V/Pi) = r

Answer 8

The third root of 3V/(4Pi)