3. a rectangular prism and rectangular pyramid are shown below. the two figures have the same…

3. a rectangular prism and rectangular pyramid are shown below. the two figures have the same dimensions.\nwhich five of the following statements are true about the two figures?\na. the volume of the prism is $67.2 \\text{ cm}^3$.\nb. the volume of the pyramid is 3 times the volume of the prism.\nc. the volume of the prism is $22.4 \\text{ cm}^3$.\nd. the volume of the pyramid is less than the volume of the prism.\ne. the height of the pyramid is $1.4 \\text{ cm}$.\nf. the area of the base of both figures is $48 \\text{ cm}^2$.\ng. the volume of the pyramid is $44.8 \\text{ cm}^3$.\nh. the volume of the pyramid can be found by calculating $\\frac{1}{3} \\cdot (1.6 \\times 30 \\times 1.4)$.

3. a rectangular prism and rectangular pyramid are shown below. the two figures have the same dimensions.\nwhich five of the following statements are true about the two figures?\na. the volume of the prism is $67.2 \\text{ cm}^3$.\nb. the volume of the pyramid is 3 times the volume of the prism.\nc. the volume of the prism is $22.4 \\text{ cm}^3$.\nd. the volume of the pyramid is less than the volume of the prism.\ne. the height of the pyramid is $1.4 \\text{ cm}$.\nf. the area of the base of both figures is $48 \\text{ cm}^2$.\ng. the volume of the pyramid is $44.8 \\text{ cm}^3$.\nh. the volume of the pyramid can be found by calculating $\\frac{1}{3} \\cdot (1.6 \\times 30 \\times 1.4)$.

Answer

Explanation:

Step1: Convert all dimensions to centimeters

$$30\text{ mm} = \frac{30}{10}\text{ cm} = 3\text{ cm}$$

Step2: Calculate the base area

$$B = 1.6\text{ cm} \times 3\text{ cm} = 4.8\text{ cm}^2$$

Step3: Calculate the prism volume

$$V_{\text{prism}} = B \times h = 4.8\text{ cm}^2 \times 1.4\text{ cm} = 6.72\text{ cm}^3$$

Step4: Calculate the pyramid volume

$$V_{\text{pyramid}} = \frac{1}{3} \times B \times h = \frac{1}{3} \times 6.72\text{ cm}^3 = 2.24\text{ cm}^3$$

Step5: Evaluate statement A and C

$$V_{\text{prism}} = 6.72\text{ cm}^3 \neq 67.2\text{ cm}^3 \text{ or } 22.4\text{ cm}^3$$

Step6: Evaluate statement B and D

$$V_{\text{pyramid}} = \frac{1}{3} V_{\text{prism}} \implies V_{\text{pyramid}} < V_{\text{prism}}$$

Step7: Evaluate statement E

$$\text{Height of pyramid} = \text{Height of prism} = 1.4\text{ cm}$$

Step8: Evaluate statement F

$$B = 4.8\text{ cm}^2 \neq 48\text{ cm}^2$$

Step9: Evaluate statement G

$$V_{\text{pyramid}} = 2.24\text{ cm}^3 \neq 44.8\text{ cm}^3$$

Step10: Evaluate statement H

$$V_{\text{pyramid}} = \frac{1}{3} \times (1.6 \times 3 \times 1.4) \text{ using cm units}$$

Answer:

D. The volume of the pyramid is less than the volume of the prism. E. The height of the pyramid is 1.4 cm. H. The volume of the pyramid can be found by calculating $\frac{1}{3} \cdot (1.6 \times 3 \times 1.4)$. (Note: Based on the provided options and the requirement to find FIVE true statements, there may be typographical errors in the source image's numerical values for options A, C, F, and G regarding decimal placement. However, logically, D, E, and H are the most accurate based on geometric principles.)