Calculate Volume of Connected Rectangular Prisms: 5×9×2 Composite Shape

To solve this problem, we will calculate the volume of each rectangular prism separately and then sum these volumes:

• Rectangular Prism 1: The prism with a square base has dimensions as follows:
• Side length of the square base = 5 units
• Height = 9 units
• The volume of a rectangular prism with a square base is given by $V = \text{side}^2 \times \text{height}$.
• Substituting the given values: $V_1 = 5^2 \times 9 = 25 \times 9 = 225 \text{ cubic units}$.
• Rectangular Prism 2: The second prism's dimensions:
• Length = 3 units
• Width = 2 units
• Height = 4 units
• The volume of this rectangular prism is calculated as $V = \text{length} \times \text{width} \times \text{height}$.
• Substituting the given values: $V_2 = 3 \times 2 \times 4 = 24 \text{ cubic units}$.

Finally, adding the volumes of the two prisms gives us the total volume:

$V_{\text{total}} = V_1 + V_2 = 225 + 24 = 249 \text{ cubic units}$.

Therefore, the volume of the new shape is $249$ cubic units.