Question

performance task
an ocean engineer places cube - shaped crates on a ship as shown in the figure.
what is the volume?
part a: one student saw the boxes and said that the figure has a volume of 7 cubic units. is the student correct? explain your thinking.
part b: the ocean engineer adds more crates so that the figure becomes a rectangular prism that has a length of 3 units, a width of 3 units, and a height of 2 units. how many more crates does the ocean engineer add? show your work and explain your answer.

Explanation:

Step1: Count initial cubes

By counting the visible and non - hidden cubes in the figure, we find there are 8 cubes. Each cube has a volume of 1 cubic unit. So the initial volume is 8 cubic units. The student who said 7 cubic units is incorrect.

Step2: Calculate volume of final prism

The volume formula for a rectangular prism is $V = l\times w\times h$. Given $l = 3$, $w = 3$, and $h = 2$, we have $V=3\times3\times 2=18$ cubic units. Since each crate has a volume of 1 cubic unit, the total number of crates in the final prism is 18.

Step3: Find number of added crates

We know there were initially 8 crates. To find the number of added crates, we subtract the initial number of crates from the final number of crates. Let $n$ be the number of added crates. Then $n=18 - 8=10$.

Answer:

Part A: The student is incorrect. The figure has 8 cubic units of volume as there are 8 cube - shaped crates.
Part B: The ocean engineer adds 10 more crates.