can someone please tell me on what exactly is the relation between the surface area of a sphere and the surface area of the curved section of the cylinder!!!!!!!!
help is greatly appreciated
Surface Area of a Sphere: $\displaystyle 4\pi r^2$
If you open up the cylinder and consider only the curved area, then this is in a shape of a rectangle. The area would be length multiplied by width. The length would be the circumference thus $\displaystyle 2\pi r$ and the width would be an arbitrary variable, lets call it $\displaystyle h$. Thus surface area of the curved section of the cylinder: $\displaystyle 2\pi r h$
There isn't a direct relationship which links both and allows one to be calculated through the other and vice versa.
Hello matrefIf the sphere fits exactly into the cylinder so that their radii are equal, and the height ($\displaystyle h$) of the cylinder is equal to the diameter ($\displaystyle 2r$) of the sphere, then the surface area of the sphere is $\displaystyle 4\pi r^2$, and the curved surface area of the cylinder $\displaystyle = 2\pi rh = 2\pi r\cdot 2r = 4\pi r^2$. In other words, the surface areas are equal.
Grandad