Question

felicia has a jewelry box in the shape of a rectangular prism that has a volume of 72 cubic inches. the box is 2 inches tall. decide if the jewelry box could have each given length and width. choose yes or no for each length and width combination. length: 24 inches; width: 12 inches - yes - no length: 12 inches; width: 6 inches - yes - no length: 12 inches; width: 3 inches - yes - no length: 10 inches; width: 7 inches - yes - no length: 9 inches; width: 4 inches - yes - no length: 6 inches; width: 6 inches - yes - no

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. Given $h = 2$ inches and $V=72$ cubic inches, we can find the area of the base $A=l\times w$ using the formula $A=\frac{V}{h}$.

Step2: Calculate the area of the base

Substitute $V = 72$ and $h = 2$ into the formula $A=\frac{V}{h}$. So, $A=\frac{72}{2}=36$ square inches.

Step3: Check each length - width combination

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

eq36$. So, the answer is No.

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

eq36$. So, the answer is No.

1. For length $l = 12$ inches and width $w = 3$ inches, $l\times w=12\times3 = 36$. So, the answer is Yes.
2. For length $l = 10$ inches and width $w = 7$ inches, $l\times w=10\times7 = 70

eq36$. So, the answer is No.

1. For length $l = 9$ inches and width $w = 4$ inches, $l\times w=9\times4 = 36$. So, the answer is Yes.
2. For length $l = 6$ inches and width $w = 6$ inches, $l\times w=6\times6 = 36$. So, the answer is Yes.

Answer:

Length: 24 inches; Width: 12 inches: No
Length: 12 inches; Width: 6 inches: No
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