Sid is packing crushed ice into a cone-shaped cup. The cone has a height of 5 in . Its base has a diameter of 4 in . What is the volume of the cone? SHOW YOUR WORK ON THE PAGE.

To find the volume of a cone, you can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius of the base, and \( h \) is the height of the cone. 1. **Find the radius**: The diameter of the cone is 4 inches, so the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ inches} \] 2. **Substitute in the values**: - Height \( h = 5 \) inches - Radius \( r = 2 \) inches 3. **Calculate the volume**: \[ V = \frac{1}{3} \pi (2)^2 (5) \] \[ V = \frac{1}{3} \pi (4)(5) \] \[ V = \frac{1}{3} \pi (20) \] \[ V = \frac{20\pi}{3} \] Thus, the volume of the cone is approximately: \[ V \approx \frac{20 \times 3.14}{3} \approx 20.94 \text{ cubic inches} \] So, the volume of the cone-shaped cup is \( \frac{20\pi}{3} \) cubic inches or about 20.94 cubic inches!