Question:
Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.
Solution:
We have the following figure to visualize the situation
Let the radius of the sphere is r. Therefore, the surface area of the sphere is
$S=4 \pi \times r^{2}$
$=4 \pi r^{2}$
The circumscribed cylinder of the sphere must have radius r cm and height 2r cm. Therefore, the curved surface area of the cylinder is
$S_{1}=2 \pi r \times 2 r$
$=4 \pi r^{2}$
Hence, S and S1 are same. Thus the proof is complete.