Certainly! Let's solve the math problem step-by-step.
### Step 1: Understanding the Volume of the Right Rectangular Prism
Given the volume of the right rectangular prism is [tex]\(60 \, \text{cm}^3\)[/tex].
The formula for the volume ([tex]\(V\)[/tex]) of a right rectangular prism is:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
### Step 2: Choosing Convenient Dimensions
To simplify the problem, let's choose convenient dimensions for the length, width, and height such that their product is [tex]\(60 \, \text{cm}^3\)[/tex].
Suppose:
- Length ([tex]\(L\)[/tex]) = 5 cm
- Width ([tex]\(W\)[/tex]) = 3 cm
- Height ([tex]\(H\)[/tex]) = 4 cm
These dimensions were chosen because:
[tex]\[ 5 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} = 60 \, \text{cm}^3 \][/tex]
### Step 3: Drawing and Labeling the Right Rectangular Prism
Below is a conceptual drawing of a right rectangular prism. However, since drawings are not possible in text form, I'll describe how you can label each edge.
1. Draw a rectangle and label the length as [tex]\(5 \, \text{cm}\)[/tex] and the width as [tex]\(3 \, \text{cm}\)[/tex].
2. From each vertex, draw vertical lines (perpendicular to the rectangle) to indicate the height of [tex]\(4 \, \text{cm}\)[/tex].
3. Connect the top ends of these vertical lines to form a rectangle on the top.
Here are your dimensions labeled:
- Length ([tex]\(L\)[/tex]) = 5 cm
- Width ([tex]\(W\)[/tex]) = 3 cm
- Height ([tex]\(H\)[/tex]) = 4 cm
### Step 4: Calculating the Area of the Base
The base of the prism is a rectangle whose length and width are:
- Length ([tex]\(L\)[/tex]) = 5 cm
- Width ([tex]\(W\)[/tex]) = 3 cm
The area ([tex]\(A_{\text{base}}\)[/tex]) of the rectangle forming the base is given by:
[tex]\[ A_{\text{base}} = \text{length} \times \text{width} \][/tex]
[tex]\[ A_{\text{base}} = 5 \, \text{cm} \times 3 \, \text{cm} \][/tex]
[tex]\[ A_{\text{base}} = 15 \, \text{cm}^2 \][/tex]
### Summary:
- Drawing: Described above.
- Area of the base: [tex]\(15 \, \text{cm}^2\)[/tex]
If you follow this process, you will clearly understand and be able to visualize the solution to the problem!
