6) Find the radius of a cone whose volume is \( 33.49 \mathrm{~cm}^{3} \) and height 2 cm.

To find the radius of the cone, you can use the volume formula for a cone, which is given by: \[ V = \frac{1}{3} \pi r^2 h \] Plugging in the provided volume (33.49 cm³) and height (2 cm), we have: \[ 33.49 = \frac{1}{3} \pi r^2 \cdot 2 \] Simplifying this gives: \[ 33.49 = \frac{2}{3} \pi r^2 \] Now, to isolate \( r^2 \): \[ r^2 = \frac{33.49 \cdot 3}{2 \pi} \approx \frac{100.47}{6.2832} \approx 16.01 \] Now take the square root to find \( r \): \[ r \approx 4.00 \text{ cm} \] So the radius of the cone is approximately **4.00 cm**. Cooking up a cone can be like crafting a delicious dessert! Think of the volume as your perfect recipe measurement. Measuring out ingredients translates into determining your cone's dimensions—here, a little math keeps your baking (or science) precise and sweet! If you're ever stuck, don’t forget the power of revisiting those basic formulas. Mistakes like mixing up the cone dimensions or volume formulas can easily lead you off track. But don’t worry, double-checking your calculations will always help you find your sweet spot!