Question

rectangular prism that has a volume of 72 cubic inches. the box is 2 inches tall. length: 24 inches; width: 12 inches length: 12 inches; width: 6 inches length: 12 inches; width: 3 inches length: 10 inches; width: 7 inches length: 9 inches; width: 4 inches length: 6 inches; width: 6 inches choose yes or no for each length and width combination.

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. Here $h = 2$ inches and $V=72$ cubic inches. We need to check if $l\times w\times2=72$, or $l\times w = 36$.

Step2: Check each length - width combination

• For length = 24 inches and width = 12 inches, $l\times w=24\times12 = 288

eq36$, so No.

• For length = 12 inches and width = 6 inches, $l\times w=12\times6 = 72

eq36$, so No.

• For length = 12 inches and width = 3 inches, $l\times w=12\times3 = 36$, so Yes.
• For length = 10 inches and width = 7 inches, $l\times w=10\times7 = 70

eq36$, so No.

• For length = 9 inches and width = 4 inches, $l\times w=9\times4 = 36$, so Yes.
• For length = 6 inches and width = 6 inches, $l\times w=6\times6 = 36$, so Yes.

Answer:

Length: 12 inches; Width: 3 inches - Yes
Length: 10 inches; Width: 7 inches - No
Length: 9 inches; Width: 4 inches - Yes
Length: 6 inches; Width: 6 inches - Yes
Length: 24 inches; Width: 12 inches - No
Length: 12 inches; Width: 6 inches - No