A \(20 \times 40\) -ft. swimming pool is \(4 \mathrm{ft}\). deep and is filled to the brim, a) How many cubic feet of water are in the pool? b) If one gallon is \(0.13\) cubic feet, how many gallons of water are in the pool? c) If water weighs approximately \(62.4 \mathrm{lb} / \mathrm{cu}\). ft., what is the approximate weight of water in the pool?

A regular pyramid has a pentagon for its base. (a) Show that the area of the base is given by the formula \(\beta=(5 / 4) \mathrm{e}^{2} \tan 54^{\circ}\) where \(e=\) an edge of the base. (a) If the slant height of the pyramid makes an angle of \(54^{\circ}\) with the altitude of the pyramid, show that the altitude is given by the formula \(\mathrm{h}=(\mathrm{e} / 2)\). (b) Using the formulas of part a and \(b\), write a formula for the volume of the pyramid in terms of the base edge e.

What are the dimensions of a solid cube whose surface area is numerically equal to its volume?

Let \(\mathrm{ABCD}\) be a regular tetrahedron with each edge of length 2\. Let \(\underline{A E}\) be perpendicular to the base, and assume that \(\mathrm{CE}=(2 / 3) \mathrm{CF}\). (See figure). In $\Delta \mathrm{BCD}, \underline{C F} \perp \underline{\mathrm{BD}}$. a) What is the length of \(\mathrm{CF} ? \mathrm{~b}\) ) What is the length of $\mathrm{CE} ? \mathrm{c}\( ) What is the length of \)A E ?$ d) What is the base area of \(\triangle B C D ?\) e) What is the volume of the tetrahedron?

Show that two prisms have equal volumes if their bases have equal areas and their altitudes are equal.

The base of a right prism, as shown in the figure, is an equilateral triangle, each of whose sides measures 4 units. The altitude of the prism measures 5 units. Find the volume of the prism. [Leave answer in radical form.]