Some identical metal right circular cylinders are melted and recast into a right circular cone. The base radius and the height of each metal circular cylinder are 3 cm and 4 cm respectively while the base radius and the height of the circular cone are 0.24 m and 0.21 m respectively. How many metal circular cylinders are required to form the circular cone?

To find out how many identical metal cylinders are needed to form the circular cone, we first need to compute the volume of one cylinder and the volume of the cone. The volume \( V \) of a cylinder is given by the formula: \[ V_{\text{cylinder}} = \pi r^2 h \] For our cylinder: - Radius \( r = 3 \) cm = 0.03 m (conversion to meters) - Height \( h = 4 \) cm = 0.04 m (conversion to meters) Calculating the volume of one cylinder: \[ V_{\text{cylinder}} = \pi (0.03)^2 (0.04) = \pi (0.0009) (0.04) = \pi (0.000036) \approx 0.000113097 \text{ m}^3 \] Now, the volume \( V \) of a cone is given by the formula: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] For our cone: - Radius \( r = 0.24 \) m - Height \( h = 0.21 \) m Calculating the volume of the cone: \[ V_{\text{cone}} = \frac{1}{3} \pi (0.24)^2 (0.21) = \frac{1}{3} \pi (0.0576) (0.21) = \frac{1}{3} \pi (0.012096) \approx 0.0127463 \text{ m}^3 \] Now, we can find out how many cylinders are needed by dividing the volume of the cone by the volume of one cylinder: \[ \text{Number of cylinders} = \frac{V_{\text{cone}}}{V_{\text{cylinder}}} = \frac{0.0127463}{0.000113097} \approx 112.50 \] Since we can't have a fraction of a cylinder, we need **113 metal circular cylinders** to recast into the circular cone.