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Problem 854

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.]

Expert verified

The volume of the right prism with an equilateral triangular base of side 4 units and altitude of 5 units is \(20\sqrt{3}\) cubic units.

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Chapter 49

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Chapter 49

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Chapter 49

Show that the volume of any pyramid is equal to one-third the product of the area of the base and altitude. Assume that the volume of a triangular pyramid equals one-third the product of the base area and the altitude.

Chapter 49

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.

Chapter 49

Find the volume of a pyramid whose base is an equilateral triangle with side 10 and whose altitude is 20 .

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