Chapter 9.2, Problem 33E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

The street department’s storage building, which is used to store the rock, gravel, and salt used on the city’s roadways, is built in the shape of a regular hexagonal pyramid. The altitude of the pyramid has the same length as any side of the base. If the volume of the interior is

To determine

**To find:**

The length of the altitude and of each side of the base to the nearest foot.

Explanation

**Given:**

A regular hexagonal pyramid and the altitude of the pyramid has the same length as any side of the base i.e.

**Properties Used:**

A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

The lateral area

The total surface area

According to the Pythagorean theorem, in a right-angled triangle

In a regular pyramid, the lengths of the apothem

The perimeter of the square is four times the side.

The volume

**Calculation:**

Since, the sides of the hexagonal base measure

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