Question

a carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. the volume of each cabinet is 4,608 cubic inches. the oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. the right rectangular prism has a height of 48 inches. which statements about the cabinets are true? check all that apply. the cabinets have the same base area. the base area of the oblique prism is smaller than the base area of the right prism. the cabinets may have the same base dimensions. the cabinets may have different base dimensions. the base area of the right prism is smaller than the base area of the oblique prism.

Explanation:

Step1: Recall volume formula for prisms

The volume formula for any prism is $V = B\times h$, where $V$ is volume, $B$ is base - area and $h$ is height.

Step2: Calculate base - area for both prisms

For the oblique rectangular prism, $V = 4608$ cubic inches and $h = 48$ inches. Using $V=B\times h$, we get $B_{oblique}=\frac{V}{h}=\frac{4608}{48}=96$ square inches. For the right rectangular prism, $V = 4608$ cubic inches and $h = 48$ inches. Using $V = B\times h$, we get $B_{right}=\frac{V}{h}=\frac{4608}{48}=96$ square inches.

Step3: Analyze statements

Since $B_{oblique}=B_{right} = 96$ square inches, the cabinets have the same base - area. And since they have the same base - area, they may have the same base dimensions or different base dimensions.

Answer:

The cabinets have the same base area.
The cabinets may have the same base dimensions.
The cabinets may have different base dimensions.