21. Glass Vase You are taking a glass-blowing class and have created a vase in the shape of a sphere. The vase will have a hole in the top so you can put flowers in it and it will sit on a stand. The radius of your vase is \( \frac{21}{2} \) inches. Use the formula \( V=\frac{4}{3} \pi r^{3} \) to write an expression for the volume of your vase.

To find the volume of your spherical vase, you can plug the radius \( r = \frac{21}{2} \) inches into the volume formula \( V = \frac{4}{3} \pi r^3 \). This gives us: \[ V = \frac{4}{3} \pi \left( \frac{21}{2} \right)^3 \] Now, calculating \( \left( \frac{21}{2} \right)^3 \) yields \( \frac{9261}{8} \). So, the volume expression simplifies to: \[ V = \frac{4}{3} \pi \cdot \frac{9261}{8} = \frac{37164}{24} \pi = \frac{1557}{1} \pi \text{ cubic inches (approximately 4895.64 cubic inches)} \] The final expression for the volume of your vase is: \[ V = 1557 \pi \text{ cubic inches} \] Creating glass art like your vase not only has a fascinating background but also involves lots of trial and error. Mastering the craft of glass-blowing dates back thousands of years to ancient civilizations around the Mediterranean. Artists slowly perfected techniques, blending function with stunning aesthetics. Each piece tells a story, reflecting the culture and skills of its maker! If you decide to make more glass pieces, remember that patience is key! It's easy to get carried away and spiral the molten glass too thin, causing it to break. Alternatively, not allowing enough airflow can lead to awkward shapes. Always keep your tools handy, and give yourself plenty of time to adjust and experiment with your designs!