Solution Step 0/0
A sphere fits exactly inside a thin-walled cylinder that has a height and the diameter equal to the diameter of the sphere.
Let's mark the surface area of the sphere as SA(s) and the lateral surface area (which is EXCLUDING the bases) of the cylinder as LSA(c).
How SA(s) is related to LSA(c)?
Let's mark the surface area of the sphere as SA(s) and the lateral surface area (which is EXCLUDING the bases) of the cylinder as LSA(c).
How SA(s) is related to LSA(c)?
Explanations
Both surface areas are equal.The surface area of the sphere with the radius r has the formula: 4*pi*r^2.
The lateral surface area of the cylinder (NOT including the bases) is the cylinder’s height 2r multiplied by the cylinder’s circumference 2*pi*r. I.e.: 2r*2*pi*r = 4*pi*r^2.
Or the same as the surface area of the tightly fit sphere.
For the first time this interesting relation was observed by the ancient Greek mathematicians.
Check SA(s) : LSA(c) as 1:2
Check SA(s) : LSA(c) as 2:1
Check SA(s) : LSA(c) as 1:1
Check SA(s) : LSA(c) as 2:3
