To find the volume and the surface area of a rectangular prism with dimensions 2 inches, 6 inches, and 4 inches, we can use the following formulas:
Volume (V) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]
Surface Area (SA) of a rectangular prism is calculated using the formula: \[ SA = 2 \times (\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length}) \]
Step 1: Volume Calculation
Using the dimensions:
- Length = 6 in
- Width = 4 in
- Height = 2 in
\[ V = 6 \times 4 \times 2 \] \[ V = 48 \text{ cubic inches} \]
Step 2: Surface Area Calculation
Using the same dimensions, we calculate the surface area: \[ SA = 2 \times (6 \times 4 + 4 \times 2 + 2 \times 6) \] Calculating each term:
- \(6 \times 4 = 24\)
- \(4 \times 2 = 8\)
- \(2 \times 6 = 12\)
Now plug those into the formula: \[ SA = 2 \times (24 + 8 + 12) = 2 \times 44 = 88 \text{ square inches} \]
Final Answers
- Volume: 48 cubic inches
- Surface Area: 88 square inches
So, the volume is \(48\) cubic inches.