Frustum of a Cone

If we cut the cone with a plane which is parallel to its base and remove the cone then the remaining piece will be the Frustum of a Cone.

Volume of the frustum of the cone\dfrac{1}{3}\pi h(R^2+r^2+Rr)
The curved or Lateral surface area of the frustum of the cone\pi l(R+r)
Total surface area of the frustum of the coneArea of the base + Area of the top + Lateral surface area  \pi R^2+\pi r^2+\pi l(R+r)
Slant height of the frustuml=\sqrt{h^2+(R-r)^2}

Example

Find the lateral surface area of the given frustum of a right circular cone. 

Solution

Given,  r =1.8 in.

R=4 in.

l = 4.5 in.

The lateral surface area of the frustum of the cone =\pi l\ (R+r)

=\pi\times4.5\ (4+1.8)

=3.14\times4.5\times5.8

=81.95 sq. in.

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