Question
Find the surface area of the prism. You have a cube. The length is 7 in, width is 6 in, and height is 3 in.
Answers
GPT-4o mini
It looks like there might be a misunderstanding in the description of the shape. A cube has equal lengths for all sides, but you provided dimensions of length (7 in), width (6 in), and height (3 in). These dimensions actually describe a rectangular prism (also known as a cuboid).
To find the surface area of a rectangular prism, you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Substituting in your dimensions:
- \( l = 7 \) in,
- \( w = 6 \) in,
- \( h = 3 \) in.
Now, calculate the areas of the three pairs of opposite faces:
1. \( lw = 7 \times 6 = 42 \)
2. \( lh = 7 \times 3 = 21 \)
3. \( wh = 6 \times 3 = 18 \)
Now, plug these values into the surface area formula:
\[
\text{Surface Area} = 2(42 + 21 + 18)
\]
Calculate the sum inside the parentheses:
\[
42 + 21 + 18 = 81
\]
Now multiply by 2:
\[
\text{Surface Area} = 2 \times 81 = 162 \, \text{in}^2
\]
Thus, the surface area of the rectangular prism is **162 square inches**.
To find the surface area of a rectangular prism, you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Substituting in your dimensions:
- \( l = 7 \) in,
- \( w = 6 \) in,
- \( h = 3 \) in.
Now, calculate the areas of the three pairs of opposite faces:
1. \( lw = 7 \times 6 = 42 \)
2. \( lh = 7 \times 3 = 21 \)
3. \( wh = 6 \times 3 = 18 \)
Now, plug these values into the surface area formula:
\[
\text{Surface Area} = 2(42 + 21 + 18)
\]
Calculate the sum inside the parentheses:
\[
42 + 21 + 18 = 81
\]
Now multiply by 2:
\[
\text{Surface Area} = 2 \times 81 = 162 \, \text{in}^2
\]
Thus, the surface area of the rectangular prism is **162 square inches**.