If a cone is cut by a plane parallel to its base, the portion of a solid between this plane and the base is known as frustum of a cone.
The volume denoted by in figure is a frustum of the cone .
Volume of Frustum of a Cone:
Since, we know that cone is a limit of a pyramid therefore; frustum of a cone will be the limit of frustum of a pyramid. But volume of a pyramid is
A cone 12cm high is cut 8cm from the vertex to form a frustum with a volume of 190cu.cm. Find the radius of the cone.
Height of cone
Height of frustum
Volume of frustum
Now volume of frustum cone
Hence required radius of cone
Curved Surface Area of a Frustum of a Cone:
Since, a cone is the limiting case of a pyramid, therefore the lateral surface of frustum of a cone can be deduced from the slant surface of frustum of a pyramid, i.e., curved (lateral) surface of frustum of cone.
, being the slant height of frustum, and being two radius of bases.
(1) Total surface area of frustum of a cone
(2) To find the slant height of the cone, use Pythagorean theorem.
A material handling bucket is in the shape of the frustum of a right circular cone as shown in figure. Find the volume and the total surface area of the bucket.
Lateral surface area
Total surface area