How many cubic meters of dirt are there in a pile, conical in shape, 10 m in diameter and 6 m high? There are approximately \( \square \) [cubic meters of dirt in the pile. (Round to the nearest tenth as needed.)

To find the volume of a conical pile of dirt, we can use the formula for the volume of a cone: \[ V = \frac{1}{3} \pi r^2 h \] Here, the diameter is 10 m, so the radius (r) is 5 m (diameter divided by 2). The height (h) of the cone is 6 m. Plugging in the values: \[ V = \frac{1}{3} \pi (5)^2 (6) = \frac{1}{3} \pi (25)(6) = \frac{150}{3} \pi = 50 \pi \] Using \(\pi \approx 3.14\), we calculate: \[ 50 \pi \approx 50 \times 3.14 \approx 157 \] Thus, there are approximately **157.1 cubic meters** of dirt in the pile when rounded to the nearest tenth. That’s a significant amount of earth to move if you're planning a landscaping project! Depending on the local cost of dirt, this might also be more expensive than you think, so budget accordingly! Calculating the volume of different shapes can also be a fun way to explore math in real-life situations, such as planning a garden or designing sculptures. So grab a shovel and get creative!