A cone has a volume of 113.04 cubic meters and a radius of 3 meters. What is its height? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth. \[ h \approx \square \text { meters } \]

To find the height of the cone, we can use the volume formula for a cone: \[ V = \frac{1}{3} \pi r^2 h \] Given the volume \( V = 113.04 \) cubic meters and the radius \( r = 3 \) meters, we can substitute the known values into the formula: \[ 113.04 = \frac{1}{3} \times 3.14 \times (3^2) \times h \] Calculating \( (3)^2 = 9 \): \[ 113.04 = \frac{1}{3} \times 3.14 \times 9 \times h \] This simplifies to: \[ 113.04 = 9.42h \] Next, we solve for \( h \): \[ h = \frac{113.04}{9.42} \approx 12.00 \text{ meters} \] Thus, the height of the cone is approximately \[ h \approx 12.00 \text{ meters} \] So the final answer is: \[ h \approx 12.00 \text{ meters} \] Now, let's add some fun background info! Did you know that cones have been used since ancient times? The cone shape is not just useful; it appears in everything from architecture to ice cream cones! Their unique shape also helps them collect and distribute weight efficiently, making them a staple in engineering design. If you're diving deeper into geometry, consider exploring the fascinating world of conic sections! Conic sections include ellipses, parabolas, and hyperbolas formed by intersecting a cone with a plane. Each has unique properties and applications in physics, engineering, and even astronomy. Who knew cones could lead to such exciting discoveries?