Aright rectangular prism has these dimensions: length 1 1/3 width 5/6 height 2/3 how many cubes of side length 1/6 unit are required to completely pack the prism without any gap or overlap?

The number of cubes required is 160.

Step-by-step explanation:

The dimensions of the right rectangular prisms are

l=1\frac{1}{3} \;units

w=\frac{5}{6} \;units

h=\frac{2}{3} \;units

The volume of the right rectangular prism is

V=l\times b\times h.

We substitute the dimensions to get,

V=1\frac{1}{3}\times \frac{5}{6}\times \frac{2}{3}.

We convert the first mixed number to improper fraction,

V=\frac{4}{3}\times \frac{5}{6}\times \frac{2}{3}.

We multiply out to obtain,

V=\frac{40}{54}

V=\frac{20}{27} cubic units.

We need to determine the volume of the cube of side length,

l=\frac{1}{6} units.

The volume of a cube is given by,

V=l^3

This implies that,

V=(\frac{1}{6})^3

This gives us,

V=\frac{1}{216} cubic units.

We now divide the volume of the right rectangular prism by the volume of the cube to determine the number of cubes required.

Number\:of\:cubes=\frac{\frac{20}{27} }{\frac{1}{216} }

We simplify to get,

Number\:of\:cubes=\frac{20}{27} \div \frac{1}{216}

This implies that,

Number\:of\:cubes=\frac{20}{27} \times \frac{216}{1}

Number\:of\:cubes=20\times8

Number\:of\:cubes=160

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

answer: b

step-by-step explanation: