Double the diameter of a sphere

Dependence of different sizes of a sphere on each other

• Take a look at the relationships between the diameter, radius, surface and volume of a sphere, to make a statement later about how these sizes change when you change the diameter double.
• The diameter is the length of the path that starts on the surface of the sphere, goes through the center point and ends again on the surface on the other side. The radius is the length of the line that goes from the center point to the surface. Since the center is also in the middle of the diameter, there is a clear relationship that 2 r = d, or r = d / 2.
• The circumference of a sphere is U = 2 pi r => U = 2 pi d / 2 = pi d.
• The surface of a sphere is calculated according to the formula A_surface = 4 pi r² calculated. It follows from this: A._surface = 4 pi (d / 2)² = 4 pi (d²/ 4) = pi d^2.
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• Calculate the volume using Formula V._Bullet= (4/3) pi r³ => V_Bullet= (4/3) pi (d / 2)³ = (4/3) pi (i.e.³/ 8) = (1/6) pi d³.


Volume calculation - this is how it works for a sphere

Volume calculations are not always easy, especially when it comes to "round" ...

Now, in the next step, it is very easy to determine what happens when you double the diameter of the sphere.

Follow if you double the diameter

• The following consideration arises for the scope: U_2d = pi (2d) = 2 pi d. U_1d = pi d. U_2d/ U_1d = 2 pi d / (pi d) = 2. If you double the diameter, the circumference also doubles.
• The following applies to the surface: A._{Surface 2d}= pi (2d)² = 4 pi d² => A_{Surface 2d}/ A_{Surface 1d}= 4 pi d²/ (pi d²) = 4. The surface area of ​​a sphere quadruples when you double the diameter. Note: 2²=4. The surface depends on d² linearly.
• The following applies to the volume: V_{Sphere 2d} = (1/6) pi (2d)³ = (8/6) pi d³ = (4/3) pi d³ => V_Sphere2d/ V_{Sphere 1d} = (4/3) pi d³/ [(1/6) pi d³] = 4/3: 1/6 = 4/3 * 6/1 = 8. When the diameter is doubled, the volume increases eightfold. The volume is of d³ linearly dependent. 2³ = 8.