Exercise 28 Page 731

We have a plumb bob formed by a regular hexagonal prism and a pyramid.

We are asked to find the volume of the plumb bob. To do so we should find the volume of the prism and the volume of the pyramid. c|c Volume of a Pyramid&Volume of a Prism V= B h & V=1/3 B h In the formulas, B is the area of the base of the solids and h is the height of the solids. As we can see, both of the solids have the same hexagonal base.

To find the area of a regular hexagon, we should first find its apothem. Note that since it is a regular hexagon it consists of six equilateral triangles.

To find the value of a we will use the Pythagorean Theorem. From here we can find the area of the base using the following formula. B=n* 1/2as In the formula, a is the apothem, s is the side length of the regular polygon, and n is the number of sides of the regular polygon. Let's substitute a=sqrt(3), s=2, and n=6 into the formula and compute the area of the base. B&=6* 1/2(sqrt(3))( 2) &=6sqrt(3) Now we can find the volume of each solid by substituting the values into the formulas. c|c Volume of the Pyramid&Volume of the Prism V= 6sqrt(3)(6) & V=1/3( 6sqrt(3))(3) =36sqrt(3) & =6sqrt(3) Finally, by adding the volumes of the solids we can find the volume of the plumb bob. Therefore, the volume of the plumb bob is approximately 73 cubic centimeters.