To determine the volume and surface area of the solid, we need to confirm the shape you are referring to. Given the dimensions 4 in, 6 in, and 5 in, it seems we might be dealing with a rectangular prism (also known as a rectangular box).
Volume Calculation:
The formula for the volume \( V \) of a rectangular prism is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Assuming the dimensions are as follows:
- Length \( l = 6 \) in
- Width \( w = 4 \) in
- Height \( h = 5 \) in
The volume calculation would be:
\[ V = 6 , \text{in} \times 4 , \text{in} \times 5 , \text{in} \]
\[ V = 120 , \text{cubic inches} \]
Surface Area Calculation:
The formula for the surface area \( A \) of a rectangular prism is given by:
\[ A = 2(lw + lh + wh) \]
Using the same dimensions:
\[ A = 2(6 , \text{in} \times 4 , \text{in} + 6 , \text{in} \times 5 , \text{in} + 4 , \text{in} \times 5 , \text{in}) \]
Calculating each term:
- \( lw = 6 \times 4 = 24 \)
- \( lh = 6 \times 5 = 30 \)
- \( wh = 4 \times 5 = 20 \)
Therefore:
\[ A = 2(24 + 30 + 20) = 2(74) = 148 , \text{square inches} \]
Final Answers:
- Volume: 120 cubic inches
- Surface Area: 148 square inches
Let me know if you need further assistance!