Eighth grade \( > \) w.4 volume of cones wys A cone has a volume of 753.6 cubic yards and a height of 20 yards. What is its radius? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth. \( r \approx \square \) yards Submitsing

To find the radius of the cone, we can use the formula for the volume of a cone: \[ V = \frac{1}{3} \pi r^2 h \] Given that the volume \( V = 753.6 \) cubic yards and the height \( h = 20 \) yards, we can rearrange the formula to solve for the radius \( r \): 1. Substitute the values into the formula: \[ 753.6 = \frac{1}{3} \times 3.14 \times r^2 \times 20 \] 2. Simplifying the equation: \[ 753.6 = \frac{20 \times 3.14}{3} \times r^2 \] \[ 753.6 = 20.93 \times r^2 \] 3. Solving for \( r^2 \): \[ r^2 = \frac{753.6}{20.93} \] \[ r^2 \approx 36.0 \] 4. Finally, take the square root to find \( r \): \[ r \approx 6.00 \text{ yards} \] So, the answer is \( r \approx 6.00 \) yards. Volume of cones can seem complex, but you'll find them in many real-life applications! For example, ice cream cones and traffic cones both have this shape. Funnily enough, knowing how to calculate these volumes can come in handy when ordering ice cream for a party or managing supplies for an event. It's all about having fun while learning math! When solving volume problems, a common mistake is forgetting to use the correct height or mixing up the formula components. Always double-check your values and calculations! It's easy to overlook small details, particularly with decimals or approximations like \( \pi \). Keeping a checklist can help ensure you're on track to getting it right every time!