The cross-section of the ball is an area of 16пcm. is at a distance of 3 cm from the center of the ball. find its surface area.

Knowing the sectional area, we determine the radius of the section circle.

Ssection = π * r ^ 2 = π * O1A ^ 2.

O1A2 = Ssection / π = 16 * π / π = 16.

О1А = 4 cm.

Triangle OO1A is rectangular, then, by the Pythagorean theorem, OA ^ 2 = R ^ 2 = OO1 ^ 2 + AO1 ^ 2 = 9 + 16 = 25.

R = 5 cm.

Then the surface area of the ball is equal to:

Spov = 4 * π * R ^ 2 = 100 * π cm2.

Answer: The surface area of the ball is 100 * π cm2.



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