Questions: pa1 pa2 pa3 pa4 pa5 pa6 pa7

pa1 pa2 pa3 pa4 pa5 pa6 pa7
Transcript text: pa_1 pa_2 pa_3 pa_4 pa_5 pa_6 pa_7
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Solution

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Solution Steps

Step 1: Identify the Shape and Dimensions

The given shape is a rectangular prism with a triangular prism on top. The dimensions provided are:

  • Rectangular prism: 5 units (length), 3 units (width), 2 units (height)
  • Triangular prism: 3 units (base), 3 units (height), 1.5 units (depth)
Step 2: Calculate the Volume of the Rectangular Prism

The volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] \[ V = 5 \times 3 \times 2 = 30 \text{ cubic units} \]

Step 3: Calculate the Volume of the Triangular Prism

The volume \( V \) of a triangular prism is given by: \[ V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{depth} \] \[ V = \frac{1}{2} \times 3 \times 3 \times 1.5 = \frac{1}{2} \times 13.5 = 6.75 \text{ cubic units} \]

Final Answer

The total volume of the combined shape is the sum of the volumes of the rectangular prism and the triangular prism: \[ V_{\text{total}} = 30 + 6.75 = 36.75 \text{ cubic units} \]

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