The Best Way To Find The Radius Of A Sphere

If you have a sphere with a diameter of 16 cm, find the radius by dividing 16/2 to get 8 cm. If the diameter is 42, then the radius is 21.

If you have a sphere with a circumference of 20 m, find the radius by dividing 20/2π = 3. 183 m. Use the same formula to convert between the radius and circumference of a circle.

If you have a sphere with a volume of 100 inches3, solve for the radius as follows: ((V/π)(3/4))1/3 = r ((100/π)(3/4))1/3 = r ((31. 83)(3/4))1/3 = r (23. 87)1/3 = r 2. 88 in = r

If you have a sphere with a surface area of 1,200 cm2, solve for the radius as follows: √(A/(4π)) = r √(1200/(4π)) = r √(300/(π)) = r √(95. 49) = r 9. 77 cm = r

Diameter (D): the distance across the sphere – double the radius. Diameter is the length of a line through the center of the sphere: from one point on the outside of the sphere to a corresponding point directly across from it. In other words, the greatest possible distance between two points on the sphere. Circumference (C): the one-dimensional distance around the sphere at its widest point. In other words, the perimeter of a spherical cross-section whose plane passes through the center of the sphere. Volume (V): the three-dimensional space contained inside the sphere. It is the “space that the sphere takes up. “[6] X Research source Surface Area (A): the two-dimensional area on the outside surface of the sphere. The amount of flat space that covers the outside of the sphere. Pi (π): a constant that expresses the ratio of the circle’s circumference to the circle’s diameter. The first ten digits of Pi are always 3. 141592653, although it is usually rounded to 3. 14.

D = 2r. As with circles, the diameter of a sphere is twice the radius. C = πD or 2πr. As with circles, the circumference of a sphere is equal to π times the diameter. Since the diameter is twice the radius, we can also say that the circumference is twice the radius times π. V = (4/3)πr3. The volume of a sphere is the radius cubed (times itself twice), times π, times 4/3. A = 4πr2. The surface area of a sphere is the radius squared (times itself), times π, times 4. Since the area of a circle is πr2, it can also be said that the surface area of a sphere is four times the area of the circle formed by its circumference.

This process is easier to understand by following along with an example. For our purposes, let’s say that we have a sphere centered around the (x,y,z) point (4, -1, 12). In the next few steps, we’ll use this point to help find the radius.

For our example problem, let’s say that we know that the point (3, 3, 0) lies on the surface of the sphere. By calculating the distance between this point and the center point, we can find the radius.

In our example, we would plug in (4, -1, 12) for (x1,y1,z1) and (3, 3, 0) for (x2,y2,z2), solving as follows: d = √((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2) d = √((3 - 4)2 + (3 - -1)2 + (0 - 12)2) d = √((-1)2 + (4)2 + (-12)2) d = √(1 + 16 + 144) d = √(161) d = 12. 69. This is the radius of our sphere.

By squaring both sides of this equation, we get r2 = (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2. Note that this is essentially equal to the basic sphere equation r2 = x2 + y2 + z2 which assumes a center point of (0,0,0).