Questions: Work out the volume of this solid (made up of a cuboid and a half cylinder). Give your answer to two decimal places. Include units (cm^3) in your answer.

Solution Steps

The volume \( V \) of a cuboid is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]

Given:

• Length = 15.4 cm
• Width = 14.3 cm
• Height = 13.1 cm

\[ V_{\text{cuboid}} = 15.4 \, \text{cm} \times 14.3 \, \text{cm} \times 13.1 \, \text{cm} \] \[ V_{\text{cuboid}} = 2883.002 \, \text{cm}^3 \]

The volume \( V \) of a cylinder is given by the formula: \[ V = \pi r^2 h \]

Since we have a half cylinder, we need to divide the volume by 2.

Given:

• Diameter = 14.3 cm, so Radius \( r \) = 7.15 cm
• Height \( h \) = 15.4 cm

\[ V_{\text{cylinder}} = \pi \times (7.15 \, \text{cm})^2 \times 15.4 \, \text{cm} \] \[ V_{\text{cylinder}} = \pi \times 51.1225 \, \text{cm}^2 \times 15.4 \, \text{cm} \] \[ V_{\text{cylinder}} = 2476.990 \, \text{cm}^3 \]

Since it's a half cylinder: \[ V_{\text{half cylinder}} = \frac{2476.990 \, \text{cm}^3}{2} \] \[ V_{\text{half cylinder}} = 1238.495 \, \text{cm}^3 \]

The total volume \( V_{\text{total}} \) is the sum of the volume of the cuboid and the volume of the half cylinder.

\[ V_{\text{total}} = V_{\text{cuboid}} + V_{\text{half cylinder}} \] \[ V_{\text{total}} = 2883.002 \, \text{cm}^3 + 1238.495 \, \text{cm}^3 \] \[ V_{\text{total}} = 4121.497 \, \text{cm}^3 \]

Final Answer