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.

Answer 1

Answer:

1.The cabinets have the same base area

2.The cabinets may have same base dimension

3.The cabinets may have different base dimension.

Step-by-step explanation:

We are given that  

Volume of each cabinet=4,608 cubic inches.

Height of oblique rectangular prism=48 in

Edge length of oblique rectangular prism=64 in

Height of right rectangular prism=48 in

Volume of right rectangular prism=$l\times b\times h$

Where base area =$l\times b$

Using the formula  

$4608=base\;area\times 48$

Base area=$\frac{4608}{48}=96 inV^2$

Volume of oblique rectangular prism=$B\times h$

Where B=Area of base

Using the formula  

$4608=B\times 48$

$B=\frac{4608}{48}=96 in^2$

1.The cabinets have the same base area

2.The cabinets may have same base dimension

3.The cabinets may have different base dimension.

Answer 2

The true statements are:

• The cabinets have the same base area
• The cabinets may have the same base dimension
• The cabinets may have different base dimension.

The given parameters are:

• Volume = 4608 cubic inches
• Height = 48 inches

The above parameters apply to both cabinets.

Since they have the same volume and height, then both cabinets have the same base area

Given that they have the same base areas, the cabinets may or may not have the same base dimension

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