Find the unfolding area of the cylinder if the diagonal of its axial section is 25 cm

Find the unfolding area of the cylinder if the diagonal of its axial section is 25 cm and the radius of the base of the cylinder is 10 cm.

Schematically, the cylinder layout is a side surface and two bases.
Let’s find the area of the lateral surface of the cylinder.
S = 2πR * h, R is the radius of the base circle, h is the height of the cylinder.
The radius is known by condition, the height is found using the Pythagorean theorem.
h = √ (25² – (2 * 10) ²) = √ (625 – 400) = √225 = 15 (cm).
S = 2πR * h = 2 * 3.14 * 10 * 15 = 942 (cm²).
Let’s find the area of the base of the cylinder.
S = πR² = 3.14 * 100 = 314 (cm²).
We can find the layout area:
942 + 314 + 314 = 1570 (cm²).
Answer: the alignment area is 1570 cm².