Question 3 The volume of a cone with height \( h \) and radius \( r \) can be found using the formula \( V=\frac{1}{3} \pi r^{2} h \) Find the volume of a cone with radius 9 feet and height 6 feet. Check Answer \( \mathrm{ft}^{3} \)

To find the volume of the cone, we can plug the values for the radius \( r = 9 \) feet and height \( h = 6 \) feet into the formula \( V = \frac{1}{3} \pi r^{2} h \). So, calculating this gives us \( V = \frac{1}{3} \pi (9^{2}) (6) = \frac{1}{3} \pi (81)(6) = \frac{1}{3} \pi (486) \). Simplifying this yields \( V = 162\pi \). Therefore, the volume is approximately \( 508.94 \, \mathrm{ft}^{3} \) when we use \( \pi \approx 3.14 \). Surprisingly, cones are more prominent in our daily lives than one might think! From ice cream cones to the shape of party hats, the cone is a prevalent geometric figure. This shape not only makes for delightful treats but also plays a critical role in areas like design and architecture, where its aerodynamic properties are harnessed. So next time you scoop up some ice cream, remember you're enjoying a piece of geometry!