040 Review Problem - Volume comparisons of two water crystals

Problem 40
When a liquid freezes, it changes into a mass of solid bodies, each of which has a definite geometric form and is known as a crystal. Crystals are always bounded by plane surfaces, which are arranged in an orderly fashion with reference to imaginary lines drawn through the crystal and called its area. Every crystal has therefore a definite geometric form. Compare the volumes of crystals, one in the shape of a hexagonal right prism 'a' units on a side and '2a' units in altitude, and the other in the shape of two oppositely directed hexagonal regular pyramids, each 'a' units high with a common base 'a' units on a side.



004 Review Problem - Size of a column in Fingal's Cave

Problem 4
In Fingal’s Cave, on the Island of Staffa (Hebrides, Scotland), the walls are formed by basaltic prismatic columns varying in height from 18 to 36 ft. These columns, mostly hexagonal, are so perfect as to suggest the hand of man. One of the vertical columns is 29.3 ft. in height and has a base of 4.7 sq. ft. What is its volume?

The Prism

Prism is a polyhedron in which two faces are equal polygons in parallel planes, and all other faces are parallelograms. There are two types of prism; oblique prism and right prism. Oblique prism is when the axis is not perpendicular to the base and right prism if the axis is parallel to the base. In right prism, all lateral areas are rectangle.

Solids for which Volume = Area of base times Altitude

Solids in which V = Ab × h
This is a group of solids in which the volume is equal to the product of the area of the base and the altitude. Two types of solids belong to this group namely, prisms and cylinders.

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