A concrete gate post comprises a right rectangular prism having a square base and a pyrumid the top, as shown in the diagram below. The Iength of the sides of the base is 30 cm in the height of the rectangular section is 150 cm . The perpendicular height of the pyramid sectic is 8 cm .

To find the total volume of the concrete gate post, we need to calculate the volumes of both the rectangular prism (the base) and the pyramid (the top) separately, and then add them together. ### Step 1: Calculate the volume of the rectangular prism The formula for the volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] Since the base is a square, the length and width are the same. Given that the side length of the base is 30 cm and the height is 150 cm, we can calculate the volume as follows: \[ V_{\text{prism}} = 30 \, \text{cm} \times 30 \, \text{cm} \times 150 \, \text{cm} \] \[ V_{\text{prism}} = 30 \times 30 \times 150 = 135000 \, \text{cm}^3 \] ### Step 2: Calculate the volume of the pyramid The formula for the volume \( V \) of a pyramid is given by: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] The base of the pyramid is also a square with a side length of 30 cm. Therefore, the area of the base is: \[ \text{Base Area} = 30 \, \text{cm} \times 30 \, \text{cm} = 900 \, \text{cm}^2 \] The height of the pyramid is given as 8 cm. Now we can calculate the volume of the pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} \times 900 \, \text{cm}^2 \times 8 \, \text{cm} \] \[ V_{\text{pyramid}} = \frac{1}{3} \times 7200 \, \text{cm}^3 = 2400 \, \text{cm}^3 \] ### Step 3: Calculate the total volume of the gate post Now, we can find the total volume by adding the volumes of the rectangular prism and the pyramid: \[ V_{\text{total}} = V_{\text{prism}} + V_{\text{pyramid}} \] \[ V_{\text{total}} = 135000 \, \text{cm}^3 + 2400 \, \text{cm}^3 = 137400 \, \text{cm}^3 \] ### Conclusion The total volume of the concrete gate post is: \[ \boxed{137400 \, \text{cm}^3} \]