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Define pappus theorems?
theorems relating respectively to the volume and the surface area of a solid generated by the revolution of plane figure around an axis lying in the same plane. 1. when a plane figure is revolved about an axis lying in the same plane (but not cutting the area)The volume generated is equal to the product of the area and the length of the path described by the centre of gravity of the area . 2. When a plane curve is revolved about an axis lying in the same plane (but not cutting the curve) the surface area generated is equal to the product of the length of the curve and the length of the path of the centre of gravity of the curve.
Are lines on a sphere in the same plane?
Not necessarily. A plane dissecting a sphere would create a circle in that plane. so in order for the "line" to be both on the plane and the sphere the line would have to be a curve or segment of a circle.
If a right circular cone intersects a plane that passes through one of its nappes but the plane is neither parallel to the edge of the cone nor perpendicular to the cones axis the resulting curve will?
If a right circular cone intersects a plane that passes through one of its nappes, but the plane is not parallel to an edge of the cone, the resulting curve will bea(n) _____ . ellipse
What is a circle by definition?
A plane curve all equidistant from a given fixed point, the center.
What is a straight line or plane that touches a curve or curved surface at one point?
A tangent
