Given slant height, height and radius of a frustum of a cone, we have to calculate the volume and surface area of the frustum of a cone.
Frustum of cone
In geometry, a frustum is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.
If we cut a right circular cone by a plane parallel to its base, the portion of the solid between this plane and the base is known as the frustum of a cone.
Given below is a right circular cone.
The right circular cone after being cut by a plane parallel to its base results in a frustum as follows:
which has a circular base at bottom of radius R
circular upper portion with radius r
and slant height l
- Volume of frustum of cone:
Volume (V) = 1/3 * pi * h(r2 + R2 + r*R) where r = radius of smaller circle R = radius of bigger circle (or radius of base of the cone) h = height of the frustum
Curved Surface Area (CSA) = pi * l(R + r) where r = radius of smaller circle R = radius of bigger circle l = slant height of the frustum
Total Surface Area (TSA) = pi * l(R + r) + pi(R2 + r2) where r = radius of smaller circle R = radius of bigger circle l = slant height of frustum
Input : Radius of smaller circle = 3 Radius of bigger circle = 8 Height of frustum = 12 Slant height of frustum = 13 Output : Volume Of Frustum of Cone : 1218.937 Curved Surface Area Of Frustum of Cone : 449.24738 Total Surface Area Of Frustum of Cone : 678.58344 Input : Radius of smaller circle = 7 Radius of bigger circle = 10 Height of frustum = 4 Slant height of frustum = 5 Output : Volume Of Frustum of Cone : 917.34436 Curved Surface Area Of Frustum of Cone : 267.03516 Total Surface Area Of Frustum of Cone : 735.1321
Volume Of Frustum of Cone : 1218.937 Curved Surface Area Of Frustum of Cone : 449.24738 Total Surface Area Of Frustum of Cone : 678.58344
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