To find the slant height of the square pyramid, we can use the Pythagorean theorem. The slant height (\( l \)), the height of the pyramid (\( h \)), and half of the base length (\( \frac{b}{2} \)) form a right triangle.
- The height of the pyramid (\( h \)) is given as 23 cm.
- The side length of the base (\( b \)) is given as 30 cm, so half of the base length is \( \frac{b}{2} = \frac{30}{2} = 15 \) cm.
Now we can use the Pythagorean theorem:
\[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \]
Substituting the values we have:
\[ l^2 = 23^2 + 15^2 \]
Calculating \( 23^2 \) and \( 15^2 \):
\[ 23^2 = 529 \] \[ 15^2 = 225 \]
Now adding these values:
\[ l^2 = 529 + 225 = 754 \]
Next, we take the square root to find \( l \):
\[ l = \sqrt{754} \approx 27.5 \text{ cm} \]
Rounding to the nearest tenth, the slant height of the model pyramid is approximately 27.5 cm.