Lateral Surface Area of Frustum


 
 
Concept Explanation
 

Lateral Surface Area of Frustum

Lateral Surface Area of Frustum: if a cone is cut by a plane parallel to the base of the cone, then the portion between the plane and base is called the frustum of the cone. Let "h" be the height, "l" the slant height and large r_{1} and large r_{2} the radii of the ends large (r_{1}>r_{2}) of the frustum of a cone.Then we can directly find the curved surface area using given formula: Curved surface area of the frustum of cone =  large =pi (r_{1}+r_{2})l  where large l=sqrt{h^{2}+(r_{1}-r_{2})^{2}}

Example : The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Solution: R and r be the radii of the ends of the frustum. large 2pi R=18 cm and dpi{120} large 2pi r=6 cm  i.e.,  large R=frac{9}{pi }cm  and large r=frac{3}{pi }cm   Slant height l = 4cm.

Then, curved surface area large =pi (R+r)times l= pi times (frac{9}{pi} + frac{3}{pi})times 4 = 48cm^2

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