Lou has a solid clay brick in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches. If the clay weighs 1.055 ounces per cubic inch, how much does Lou's brick weigh, to the nearest ounce?

The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

Step-by-step explanation:

The given is,

               A solid clay brick in the shape of a rectangular prism.

               A length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches.

               The clay weighs 1.055 ounces per cubic

Step:1

              Formula for volume of rectangular prism,

                                  ...................(1)

            Where, w - Width of the rectangular prism

                          h - Height of rectangular prism

                           l - Length of rectangular prism

            From the given,

                         w = 3.5 inches

                          h = 2.25 inches

                           l =  8 inches

           Equation (1) becomes,

                            Volume, V = 63 cubic inches

Step:2

          Weight of brick = Volume of brick × Weight per cubic inch

                                     = 66.465 ounces

          Weight of brick = 66.465 ounces

Result:

            The weight of solid clay brick is 66.465 ounces, if solid brick with a length of 8 inches, a width of 3.5 inches, and a height of 2.25 inches and the clay weighs 1.055 ounces per cubic inch.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!