Question

select all the statements that are true about the figure. a. the figure can be built by making a 4×5×2 rectangular prism and a 4×2×2 rectangular prism. b. the figure can be built by making a 2×2×5 rectangular prism and a 5×4×4 rectangular prism. c. the figure can be built by making a 4×3×2 rectangular prism and a 4×2×4 rectangular prism. d. the volume of the figure can be determined by adding the volume of each prism that was built. i can... explain how to build and determine the volumes of figures composed of rectangular prisms.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. For a composite - figure made of rectangular prisms, the total volume is the sum of the volumes of individual prisms.

Step2: Analyze option A

A $4\times5\times2$ rectangular prism and a $4\times2\times2$ rectangular prism can be combined to form the given figure. The volumes of these prisms are $V_1=4\times5\times2 = 40$ and $V_2 = 4\times2\times2=16$.

Step3: Analyze option B

A $2\times2\times5$ rectangular prism has volume $V_1=2\times2\times5 = 20$ and a $5\times4\times4$ rectangular prism has volume $V_2=5\times4\times4 = 80$. But these two prisms cannot be combined to form the given figure.

Step4: Analyze option C

A $4\times3\times2$ rectangular prism has volume $V_1=4\times3\times2=24$ and a $4\times2\times4$ rectangular prism has volume $V_2 = 4\times2\times4 = 32$. These two prisms cannot be combined to form the given figure.

Step5: Analyze option D

The volume of a composite - figure made up of rectangular prisms is indeed found by adding the volume of each prism that makes up the figure.

Answer:

A. The figure can be built by making a $4\times5\times2$ rectangular prism and a $4\times2\times2$ rectangular prism.
D. The volume of the figure can be determined by adding the volume of each prism that was built.