Question

a small hamster cage has the dimensions shown. determine the volume of the cage in cubic inches. show or explain your thinking.

Explanation:

Step1: Divide the shape into two rectangular - prisms

The first rectangular - prism has dimensions \(14\) in (height), \(16\) in (length), and \(20\) in (width). The second rectangular - prism has dimensions \(5\) in (height), \((20 - 6)\) in (length), and \(14\) in (width).

Step2: Calculate the volume of the first rectangular - prism

The volume formula for a rectangular - prism is \(V = l\times w\times h\). For the first prism, \(V_1=16\times20\times14 = 4480\) cubic inches.

Step3: Calculate the length of the second rectangular - prism

The length of the second rectangular - prism is \(20 - 6=14\) inches.

Step4: Calculate the volume of the second rectangular - prism

Using the volume formula \(V = l\times w\times h\), for the second prism, \(V_2 = 14\times14\times5=980\) cubic inches.

Step5: Calculate the total volume of the shape

The total volume \(V = V_1+V_2\). So \(V=4480 + 980=5460\) cubic inches.

Answer:

5460 cubic inches