Find the dimension of the right circular cylinder of the largest volume that can inscribed in a
Sphere of radius 10 units.
This is explained in detail at
http://jwilson.coe.uga.edu/emt725/Cylinder/OneSol.cyl.html
nothing fancy, just basic algebra.
To find the dimensions of the right circular cylinder of the largest volume that can be inscribed in a sphere of radius 10 units, we need to analyze the geometry of the problem.
Let's start by visualizing the situation. Imagine a sphere with a radius of 10 units. The right circular cylinder will be inscribed inside this sphere, which means that it will be perfectly contained within the sphere.
Now, let's consider the dimensions of the cylinder. A right circular cylinder consists of a circular base and a perpendicular height. Since the cylinder is inscribed in a sphere, the circular base will be tangent to the sphere at its widest point, and the height of the cylinder will be equal to the diameter of the sphere.
So, to find the dimensions of the cylinder, we need to find the diameter of the sphere, which is twice the radius. In this case, the radius is 10 units, so the diameter will be 2 * 10 = 20 units.
Therefore, the diameter of the cylinder will be 20 units, and since the height of the cylinder is equal to the diameter of the sphere, it will also be 20 units.
Hence, the dimensions of the right circular cylinder of the largest volume that can be inscribed in a sphere of radius 10 units are:
- Diameter = 20 units
- Height = 20 units