Question

Geometry and Modeling 4 - HS.D. 1-2

Anjali completely filled the container shown below with 616 small cubes that
were each
inch long.
Calculate the volume of the prism.
Part A
Part B
2
Create a graphical model of a prism with base 5.5 by 3.5 that
has the same volume as Part A.
Show how Anjali can calculate the volume of the prism, in cubic inches, by
using a volume formula instead of filling the container with small cubes.

Answer 1

Part A: When Anjali completely filled the container with 616 small cubs that were each 1/2 inch long, the volume of the prism was 77 cubic inches.

Part A: When we created a graphical model and calculate the volum of the prism using a volume formula instead of filling the container with small cubes, the volume of the prism was approximately 85.58 cubic inches.

How the volume of the prism is computed:

We can compute the volume of a rectangular prism using the formula:

V = lwh

Where:

The length = ;

The width = w

The length = h

When Anjali completely filled the container with 616 small cubes that were each 1/2 inch long, the volume of each cube was:

`(1)/(2)^3` =
`(1)/(8)`​ cubic inches

Thus, the total volume of the 616 cubes is:

77 cubic inches (616 ×
`(1)/(8)`)

Parrt B:

To create a graphical model of a prism with base 5.5 by 3.5 that has the same volume as Part A, we can use the formula for the volume of a rectangular prism to solve for the height of the prism and substitute as follows:

77 =(5.5)(3.5)(h)

Solving for h, we get:

h = (5.5)(3.5)77 ​≈4.4 inches

Thus, the height of the prism is approximately 4.4 inches.

Then, the volume of the prism using a volume formula instead of filling the container with small cubes is as follows:

V = lwh

Substituting the given values:

V = (5.5)(3.5)(4.4)

≈ 85.58 cubic inches