cone

034 Review Problem - Sphere dropped into a cone

034-cone-sphere.gifThe inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?
 

22 - Smallest cone that may circumscribe a sphere

Problem 22
A sphere of radius a is dropped into a conical vessel full of water. Find the altitude of the smallest cone that will permit the sphere to be entirely submerged.
 

13 - Sphere cut into a circular cone

Problem 13
A sphere is cut in the shape of a circular cone. How much of the material can be saved?
 

12 - Cone of maximum convex area inscribed in a sphere

Problem 12
Find the altitude of the circular cone of maximum convex surface inscribed a sphere of radius a.
 

Solids for which Volume = 1/3 Area of Base times Altitude

This is a group of solids in which the volume is equal to one-third of the product of base area and altitude. There are two solids that belong to this group; the pyramid and the cone.
 

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

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

$A = \pi (R + r) L$

 

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

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).