They want the cimes to hold 9 ar cubir inches of popcorn. What are two difierent possitht values for height \( h \) and radius \( r \) for the cones? One difierent possible value for height and radius for the cone is Another possible value for height and radius for the cone is Show Your Worlat

To tackle this problem, we start with the formula for the volume \( V \) of a cone, which is given by: \[ V = \frac{1}{3} \pi r^2 h \] For a cone that holds 9 cubic inches of popcorn, we set \( V = 9 \). Thus, our equation becomes: \[ 9 = \frac{1}{3} \pi r^2 h \] To find possible values of \( r \) and \( h \), we can rearrange the equation: \[ h = \frac{27}{\pi r^2} \] Now, let's plug in some values for \( r \) and calculate \( h \). 1. **First Pair:** - Let \( r = 1 \) inch. - Substituting \( r \) back into the equation: \[ h = \frac{27}{\pi \cdot (1)^2} \approx \frac{27}{3.14} \approx 8.59 \text{ inches} \] So, one possible set is \((r, h) = (1, 8.59)\). 2. **Second Pair:** - Let \( r = 2 \) inches. - Plugging in: \[ h = \frac{27}{\pi \cdot (2)^2} = \frac{27}{\pi \cdot 4} \approx \frac{27}{12.56} \approx 2.15 \text{ inches} \] This gives another possible set \((r, h) = (2, 2.15)\). So, the possible values are: - One different possible value for height and radius for the cone is \((1, 8.59)\). - Another possible value for height and radius for the cone is \((2, 2.15)\). Don't forget to check your measurements if you're actually making a cone of popcorn! 🍿✨