Which solid has a greater volume cone with a base radius of 7 cm in a height of 28 cm or a pyramid with a base area of 154 cm in a height of 28 cm

Calculate the volume of the cone:

1. V_{\text{cone}} = \frac{1}{3} \pi (7)^2 (28)

2. V_{\text{cone}} = \frac{1}{3} \pi \cdot 49 \cdot 28

3. V_{\text{cone}}=1436.76cm^3

Calculate the volume of the pyramid:

1. V_{\text{pyramid}} = \frac{1}{3} \times 154 \times 28

2. V_{\text{pyramid}} = \frac{1}{3} \times 4312

3. V_{\text{pyramid}} = 1437.33 \, \text{cm}^3

Compare the two volumes:

- V_{\text{cone}}\approx1436.76\,\text{cm}^3

- V_{\text{pyramid}} = 1437.33 \, \text{cm}^3

The pyramid has a greater volume of approximately 1437.33\,\text{cm}^3 compared to the cone's volume of 1436.76\,\text{cm}^3 .