Let's calculate the outputs step by step for each rule when the input is $-6$:

Rule 1: Subtract 7

$-6 - 7 = -13$

Rule 2: Square the input

$(-6)^2 = 36$

Rule 3: Divide by 3

$36 \div 3 = 12$

Rule 4: Divide the input into 3

$-6 \div 3 = -2$

Rule 5: Write $\pi$

Simply replace the input with the symbol $\pi$. The output is: $\pi$

Rule 6: Find the volume of a cube with side length equal to the input in cm

The side length of the cube is $-6$ cm. The volume of a cube is given by: $\text{Volume} = (\text{side length})^3 = (-6)^3 = -216 \, \text{cm}^3$

Final Outputs:

1. Rule 1: $-13$
2. Rule 2: $36$
3. Rule 3: $12$
4. Rule 4: $-2$
5. Rule 5: $\pi$
6. Rule 6: $-216 \, \text{cm}^3$

Would you like a detailed explanation for any step or further assistance?

Here are 5 related questions to extend your understanding:

1. How would the results change if the input were positive instead of negative?
2. Why is the volume of a cube negative in this context, and does it make sense physically?
3. How can fractions be expressed in simplest form when dividing?
4. What is the general formula for the volume of other 3D shapes like spheres and cones?
5. How is $\pi$ typically approximated in numerical problems?

Tip: When dealing with negative inputs, always double-check calculations with exponents and cubes to account for their effects.