Class 10 Maths Surface Areas Volumes Frustum of a Cone

Frustum of a Cone

We will take a right circular cone and remove a portion of it. There are so many ways in which we can do this. But one particular case that we are interested in is the removal of a smaller right circular cone by cutting the given cone by a plane parallel to its base. You must have observed that the glasses, used for drinking water, are of this shape.  This remaining portion of cone is called Frustum of a cone.

 

 

Let h be the height, l the slant height and r1 and r2 the radii of the ends (r1 > r2) of the frustum of a cone. Then we can directly find the volume, the curved surace area and the total surface area of frustum by using the formulae given below.

Refer ExamFear video Lessons for Proof of these formulas.

 

Numerical: The cap used by the Turks, is shaped like the frustum of a cone.  If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find area of material used for making it.

 

Solution: Surface area of the cap is π(r1 + r2)l

Total Surface Area of cap (hollow from bottom)  = π(r1 + r2)l  + π( r2)2

= 22/7 *( 10 + 4 ) * 15 + 22/7 * 4 * 4 cm2
= 710.3 cm2

 

For more examples & explanations, refer ExamFear video lessons.

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