To find the height of a rectangular prism (or box) given its length, width, and total surface area, we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2lw + 2lh + 2wh \]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 5.2 \)
- \( w = 5.2 \)
- Surface Area = 220.48
Now, we can plug in the values into the formula:
\[ 220.48 = 2(5.2)(5.2) + 2(5.2)(h) + 2(5.2)(h) \]
Calculating \( 2(5.2)(5.2) \):
\[ 2(5.2)(5.2) = 2 \times 27.04 = 54.08 \]
Now, substituting that back into the equation:
\[ 220.48 = 54.08 + 4(5.2)(h) \]
Subtract \( 54.08 \) from both sides:
\[ 220.48 - 54.08 = 4(5.2)(h) \] \[ 166.4 = 4(5.2)(h) \]
Now, simplify:
\[ 166.4 = 20.8h \]
To find \( h \), divide both sides by \( 20.8 \):
\[ h = \frac{166.4}{20.8} = 8 \]
So, the height of the rectangular prism is \( \boxed{8} \).
1 answer