Question

1. which describes the combined variation in the formula $h = \frac{v}{\pi r^2}$?

• $h$ varies directly with $v$ and inversely with $\pi$ and the square of $r$.
• $h$ varies jointly with $v$ and $r^2$.
• $h$ varies jointly with $v$ and $\pi$, and inversely with the square of $r$.
• $h$ varies directly with $v$ and inversely with the square of $r$.

Explanation:

The formula is \( h = \frac{V}{\pi r^2} \). In variation terms, when a quantity is in the numerator, it varies directly with that quantity; when in the denominator, it varies inversely. Here, h is directly proportional to V and inversely proportional to π and \( r^2 \). π is a constant, but the variation description still includes it as part of the inverse term. The other options incorrectly describe the relationships (e.g., joint variation with \( r^2 \) instead of inverse, omitting π).

Answer:

h varies directly with V and inversely with π and the square of r.