# The ball is inscribed in the cylinder. The surface area of the ball is 41. Find the total surface area of the cylinder.

The diameter of the inscribed sphere will be equal to the height of the cylinder and the diameter of the circle at its bases.

Knowing the surface area of ​​the ball, we determine its diameter.

Sp.sh. = n * D ^ 2.

D2 = Sp.w. / n = 41 / n.

D = √ (41 / p) cm.

To determine the area of ​​the lateral surface of the cylinder, we determine the circumference at the base.

L = n * D = n * √41 / n).

Then the lateral surface area is equal to: Sside = D * L = (√41 / p) * n * √41 / n = 41 cm2.

The area of ​​the base of the cylinder is: Sb = n * D ^ 2/4 = n * (√41 / n) ^ 2/4 = 41/4 cm2.

Determine the area of ​​the cylinder: S = Side + 2 * Sb = 41 + 2 * 41/4 = 61.5 cm2.

Answer: The total surface area of ​​the cylinder is 61.5 cm2.

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