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Volume of a Frustum

The perimeter...

Question

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

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Solution

The height of the frustum of the cone is h = 16 cm. The perimeters of the circular ends are 44 cm and 33 cm. Let the radii of the bottom and top circles are r₁ cm and r₂ cm respectively. Then, we have

The slant height of the bucket is

The curved/slant surface area of the frustum cone is

Hence

The volume of the frustum of the cone is

Hence

The total surface area of the frustum cone is

= 860.25 Square cm

Hence

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