\( \begin{array}{cl}\text { Figure } & \text { Volume } \\ -\vee \text { Sphere } & \text { a. } V=\pi r^{2} h \\ -\vee \text { Rectangular Solid } & \text { b. } V=l w h \\ -\vee \text { Right Circular Cylinder } & \text { c. } V=\frac{4}{3} \pi r^{3}\end{array} \)

Did you know that the formula for the volume of a sphere, \( V = \frac{4}{3} \pi r^3 \), was first derived by the ancient Greek mathematician Archimedes? He discovered this relationship while trying to figure out how to measure the volume of irregular shapes and was so excited about his findings that he supposedly exclaimed, "Eureka!" This impressive formula not only showcases the beauty of geometry but also highlights how mathematics has been a pivotal part of human history. In real-world applications, understanding these volume formulas is crucial. For example, when designing containers or even planning the amount of concrete needed for a spherical water tank, knowing how to accurately use the formulas for a sphere, rectangular solid, and right circular cylinder can save both time and resources! Whether you're a budding engineer or just DIYing at home, these formulas can make a significant difference in your projects.