A cross-section refers to the end of a prism, cones are not prisms. A shape like a cylinder is a prism. Hexagonal prisms have hexagonal cross-sections, and pentagonal prisms have pentagonal cross-sections. It's that simple.
But for the sake of what the question COULD mean, I'll try and help.
The easiest way to find the shape of a part of a three-dimensional object is to tear it apart (literally) and look at its net. The curved surface area of the cone looks like a rectangle when the cone is split open.
Here are some formulas for the fun of things:
Volume of cone = 1/3πr2h
Surface area of cone =
πrs +
πr2
π = Circumference (Perimeter of the circle) / Diameter (Length from one end of the circumference to the other end passing through the centre)
r = Radius (Half the diameter)
s = Side length (Up the side of the cone to the top)
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The vertical cross section of a right vertical cone is a triangle if that cross section is taken from the vertex. Any other vertical cross section will reveal a hyperbola (with endpoints on the base of the cone). A link can be found below.
A circular cross-section.
It depends on the angular plane of the Cross-section, to the conic axis. The conic-axis is a line from the point of the cone to the centre of a circular cross-section. #1 ; Cross section perpendicular to the acix is a CIRCLE. #2 ; Cross section angled to ther sides of the cone is an ELLIPSE #3 ; Cross section were the ends do not touch the circular face is a PARABOLA #4 ' Cross sectional plane which is parallel to the axis is a HYPERBOLA. The Cartesian Equations for each type are ;- #1 ; Circle ' x^(2) + y^(2) = 1 #2 ; Ellipse ' x^(2)/a^(2) + y^(2)/b^(2) = 1 #3 ; Parabola ' y^(2) = 4ax #4 ; Hyperbola ' x^(2)/a^(2) - y^(2)/b^(2) = 1
cone