If volumes are constructed of piled-up blocks and corresponding areas are equal, then the volumes cannot be unequal.

26) What postulate from this lesson do these words suggest?
The figure below shows two sets of piled-up blocks on a table.
27) What kind of prism does each pile of blocks appear to form?
28) What does the figure suggest about two prisms whose bases have equal areas and whose altitudes are equal?

Set II

Ream of Paper. A ream of paper contains 500 sheets and is 2 inches thick. “Letter size” paper measures 8.5 inches by 11 inches.

Thinking of a single sheet of paper as a right rectangular prism having its two sides as its bases, find each of the following measures.

38) Its altitude.
39) Its volume.
40) Its total area.

In an ancient Chinese text, the Chiu Chang Suan Shu, methods are given for finding the volumes of various solids, including the one shown below.

The faces of a “ch’ien tu” are rectangles and right triangles.

47) What kind of geometric solid is it?

Write an expression in terms of a. b and c for

48) its volume.
49) its total area.

Filling a Pool. The figure below shows a cross-section of water in a rectangular swimming pool having the shape of a right prism. The pool is 40 feet long and 20 feet wide.

54) Find the area of the cross-section in square feet.
55) Find the volume of the water in the pool in cubic feet.
56) How long would it take to fill the pool if it can be filled at the rate of 2 cubic feet per minute?