cone

Derivation of Formula for Lateral Area of Frustum of a Right Circular Cone

005 Figure for the Derivation of Formula for Lateral Area of Right Circular Cone

The lateral area of frustum of a right circular cone is given by the formula

 

AL = π (R + r)L

 

where
R = radius of the lower base
r = radius of the upper base
L = length of lateral side

 

66 - 68 Maxima and minima: Pyramid inscribed in a sphere and Indian tepee

DiffCalc 020 Square pyramid inscribed in a sphere

Problem 66

Find the largest right pyramid with a square base that can be inscribed in a sphere of radius a.

 

64 - 65 Maxima and minima: cone inscribed in a sphere and cone circumscribed about a sphere

Problem 64

A sphere is cut to the shape of a circular cone. How much of the material can be saved? (See Problem 63)

 

62 - 63 Maxima and minima: cylinder inscribed in a cone and cone inscribed in a sphere

DiffCalc 019 Cylinder inscribed in a cone

Problem 62

Inscribe a circular cylinder of maximum convex surface area in a given circular cone.

 

58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

Problem 58

For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.

 

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