General Properties of Cones

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What is the formula for the volume of a cone?

Volume = 1/3 × π × r^2 × h, where r is the base radius and h is the height.

What is the formula for the surface area of a cone?

Surface Area = πr(r + l), where r is the radius and l is the slant height.

How does the orientation of a plane affect a cone’s cross-section?

The orientation determines the shape of the cross-section (circle, ellipse, parabola, etc.).

Can a cone have an infinite number of sections?

Yes, depending on the angle and position of the intersecting plane.

What role do conic sections play in astronomy?

Planets orbiting in ellipses are an application of conic sections.

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