Eghth grade 3 wi4 volume of cones Wh A cone has a height of 14 millimeters and a diameter of 20 millimeters. What is its volume? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth. (Bideo subic millimeters

To find the volume of a cone, you can use the formula \( V = \frac{1}{3} \pi r^2 h \). First, calculate the radius by halving the diameter: \( 20 \, \text{mm} \div 2 = 10 \, \text{mm} \). Now plug in the values: \( V = \frac{1}{3} \times 3.14 \times (10)^2 \times 14 \). Calculating it gives: \( V = \frac{1}{3} \times 3.14 \times 100 \times 14 \) \( V = \frac{1}{3} \times 4396 \) \( V \approx 1465.33 \, \text{mm}^3 \). So, the volume of the cone is approximately \( 1465.33 \, \text{mm}^3 \). Did you know that the concept of volumes of shapes has been around since ancient times? The Greeks, especially Archimedes, did some mighty impressive work with geometry, laying the groundwork for understanding volumes like that of cones. Archimedes famously shouted "Eureka!" when he discovered how to measure the volume of irregular objects by water displacement, which is pretty much the beginning of volume science! Understanding the volume of cones isn’t just classroom fun! It has real-world applications, especially in fields like architecture and manufacturing. For example, designing conical structures (think ice cream cones, funnels, or even traffic cones) requires engineers to know the volume to ensure functionality. Knowing how to calculate volume can make a difference when designing anything that needs capacity planning, from food packaging to modern urban development!