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A curved shape does not have any straight lines. In a circle the line curves continually, meaning that the circle is a curved shape.
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A parabola is a curved shape that is plotted on the Cartesian plane.
The word arch can either be a noun or a verb. As a noun, it means a curved symmetrical structure. As a verb, it means to bend backwards or to provide with a curve.
A sphere has a total curved surface. A cylinder and a cone have a partial curved surface