Calculate the volume of a composite solid that consists of a cylinder with a height of 10 cm and a base radius of 3 cm, topped with a hemisphere of the same radius.

To find the volume of the composite solid, you need to calculate the volume of both the cylinder and the hemisphere and then sum them up. First, the volume of the cylinder (V_cylinder) is calculated using the formula: \[ V_{cylinder} = \pi r^2 h \] where r is the radius and h is the height. Plugging in the values: \[ V_{cylinder} = \pi (3 \, \text{cm})^2 (10 \, \text{cm}) = \pi (9) (10) = 90\pi \, \text{cm}^3 \] Next, the volume of the hemisphere (V_hemisphere) is calculated using the formula: \[ V_{hemisphere} = \frac{2}{3} \pi r^3 \] where r is the radius. Plugging in the values: \[ V_{hemisphere} = \frac{2}{3} \pi (3 \, \text{cm})^3 = \frac{2}{3} \pi (27) = 18\pi \, \text{cm}^3 \] Now, add the volumes of the cylinder and the hemisphere: \[ V_{total} = V_{cylinder} + V_{hemisphere} = 90\pi + 18\pi = 108\pi \, \text{cm}^3 \] Thus, the total volume of the composite solid is: \[ V_{total} \approx 339.29 \, \text{cm}^3 \] (using \(\pi \approx 3.14\))