In a ball with a radius of 10 cm, a cutting plane is drawn at a distance of 8 cm from the center

| September 3, 2021 | education

In a ball with a radius of 10 cm, a cutting plane is drawn at a distance of 8 cm from the center of the ball. Find: a) the cross-sectional area, b) the surface area of the ball, c) the volume of the ball

Knowing the radius of the sphere, we determine its surface area and volume.

Sball = 4 * n * R ^ 2 = 4 * n * 100 = 400 * n cm2.

Vball = 4 * n * R ^ 3/3 = 4000 * n / 3 cm3.

The cross section of a sphere is a circle with a radius of CH. Let’s connect the center of the ball with the center of the circle in the section. OH is perpendicular to the section plane. Then the triangle SON is rectangular, in which the hypotenuse SL is equal to the radius of the ball, then: CH ^ 2 = CO ^ 2 – OH ^ 2 = 100 – 84 = 36.

CH = 6 cm.

Determine the cross-sectional area.

Ssec = n * CH ^ 2 = 36 * n cm2.

Answer: The cross-sectional area is 36 * n cm2, the volume of the ball is 4000 * n / 3 cm3, the surface area of the ball is 400 * n cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.