what is the volume of this prism? all angles are right angles.\n$4\\text{ cm}$\n$5\\text{ cm}$\n$4\\text{…

Explanation:

Step1: Identify the composite prism components

The figure consists of three rectangular prisms: left, middle, and right.

Step2: Calculate the volume of the left prism

$$V_{left} = 5\text{ cm} \times 6\text{ cm} \times 3\text{ cm} = 90\text{ cm}^3$$

Step3: Calculate the volume of the middle prism

$$V_{middle} = 4\text{ cm} \times 6\text{ cm} \times (3\text{ cm} + 4\text{ cm}) = 4 \times 6 \times 7 = 168\text{ cm}^3$$

Step4: Calculate the volume of the right prism

$$V_{right} = 3\text{ cm} \times 6\text{ cm} \times 3\text{ cm} = 54\text{ cm}^3$$

Step5: Sum the volumes of all parts

$$V_{total} = 90 + 168 + 54 = 312\text{ cm}^3$$

Answer:

312 cubic centimeters