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The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by r 2 + h 2 {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where r {\displaystyle r} is the radius of the base and h {\displaystyle h} is the height.
For a circular bicone with radius R and height center-to-top H, the formula for volume becomes V = 2 3 π R 2 H . {\displaystyle V={\frac {2}{3}}\pi R^{2}H.} For a right circular cone, the surface area is
Ungula of a right circular cone. A conical ungula of height h, base radius r, and upper flat surface slope k (if the semicircular base is at the bottom, on the plane z = 0) has volume = where = is the height of the cone from which the ungula has been cut out, and
The volume of a spherical cap with a curved base can be calculated by considering two spheres with radii and , separated by some distance , and for which their surfaces intersect at =. That is, the curvature of the base comes from sphere 2.
Diagram showing a section through the centre of a cone (1) subtending a solid angle of 1 steradian in a sphere of radius r, along with the spherical "cap" (2). The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1.
Volume Cuboid: a, b = the sides of the cuboid's base ... Right circular cylinder: r = the radius of the cylinder ... Right circular solid cone: r = the radius of the ...
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The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex": =, where B 1 and B 2 are the base and top areas, and h 1 and h 2 are the perpendicular heights from the apex to the base and top planes. Considering that