Question

the cubes in each rectangular prism are the same size. each prism has at least one stack of cubes that goes up to the top. find the total number of cubes needed to completely fill each prism. then find the volume of each prism.
prism a
prism b
cubes needed to fill prism b: ______ cubes
volume of prism b: ______ cubic units
practice

Explanation:

Step1: Count layers and cubes per layer

Count the number of layers of cubes and the number of cubes in each layer to fill Prism B. Assume the base - layer has $m\times n$ cubes and there are $h$ layers.

Step2: Calculate total cubes

The total number of cubes needed to fill the prism is the product of the number of cubes in the base - layer and the number of layers. Let's assume by counting we find that the base has 4 rows and 3 columns of cubes ($m = 4$, $n=3$) and there are 5 layers ($h = 5$). The number of cubes needed to fill Prism B is $4\times3\times5=60$ cubes.

Step3: Determine volume

Since the volume of one cube is 1 cubic unit, the volume of Prism B is equal to the number of cubes needed to fill it. So the volume of Prism B is 60 cubic units.

Answer:

Cubes needed to fill Prism B: 60 cubes
Volume of Prism B: 60 cubic units