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Frustum of a Right Circular Cone
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Frustum of a Right Circular Cone
A frustum of a right circular cone has two unequal flat circular bases and a curved surface.

Let's define terms height and lateral (slant) height related to a frustum.
HEIGHT: The height or thickness of a frustum is the perpendicular distance between its two circular bases.

SLANT HEIGHT: The slant height of a frustum of a right circular cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction, of the two circular bases.
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Applications to Word Problems
Example: If the radii of the circular ends of a conical bucket which is 105 cm high, are 20 cm and 10 cm, find the capacity of the bucket (Use = 22/7).
Solution: Clearly, bucket forms a frustum of a cone such that the radii of its circular ends are r1 = 20 cm, r2 = 10 cm and height h = 105 cm.
Capacity of the bucket x Volume of the frustum
= 1/3 h(r12 + r22 + r1r2)
= 1/3 x 22/7 x 105 x (202 + 102 + 20 x 10)
= 22 x 5 x (400 + 100 + 200) = 110 x 700 cm3 = 77000 cm3
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