A cross-section is drawn in the ball at a distance of 7 cm from the center, the area of which is 576 π cm.
| April 4, 2021 | education
A cross-section is drawn in the ball at a distance of 7 cm from the center, the area of which is 576 π cm. Determine the total surface area of the ball.
Knowing the cross-sectional area of the ball, we determine the radius of the circle formed by the cross-section.
Ssec = n * BH ^ 2 = 576 * n cm2.
BH ^ 2 = 576 * n / n = 576.
BH = 24 cm.
In the right-angled triangle ВНO, according to the Pythagorean theorem, we determine the length of the hypotenuse OB, which is the radius of the circle of the ball.
OH ^ 2 = BH ^ 2 + OH ^ 2 = 24 ^ 2 + 7 ^ 2 = 576 + 49 = 625.
OB = 25 cm.
Let us determine the surface area of the ball.
Sball = 4 * n * R ^ 2 = 4 * n * OB ^ 2 = 4 * n * 625 = 2500 * n cm2.
Answer: The area of the ball is 2500 * n cm2.
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