Total Surface Area of Frustum


 
 
Concept Explanation
 

Total Surface Area of Frustum

Total Surface Area of Frustum: If a cone is cut by a plane parallel to the base of the cone, then the portion betweenthe 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 total surface are of frustum by using the formulae given below : Total surface area of the frustum of the cone large =pi l(r_{1}+r_{2})+pi r^{2}_{1}+pi r^{2}_{2}   OR it can be expressed as Total surface area of bucket large =pi left [ (r_{1}+r_{2})l+r_{2} right ]

Example: If the radii of the ends of the frustum of 24 cm high cone are 5 cm and 15 cm, find the total surface area of the bucket.

Solution: If R and r be the radii and h the height and l the slant height of the frustum of the cone, thenlarge l=sqrt{h^{2}+(R^{2}-r)^{2}}large =sqrt{(24)^{2}+(15-5)^{2}}=sqrt{676}. Hence l = 26cm

Total surface area large =pi [R^{2}+r^{2}+l(R+r)]large =frac{22}{7}[225+25+26(15+5)]large =frac{22}{7}times[250+520]=frac{22}{7}times770=2420cm^{2}

 
 
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