Question 1 ( 3 points) A rectangular prism has length of 5 cm , a width of 6 cm , and a heíght of 7 cm . What is the volume of its image if the prism is dilated by a scale factor of 4 ? \( 210 \mathrm{~cm}^{3} \) \( 64 \mathrm{~cm}^{3} \) \( 1344 \mathrm{~cm}^{3} \) \( 13,440 \mathrm{~cm}^{3} \). Hide hint for Question 1 Find the volume of the pre-image first. Remember that the scale factor must be cubed for volume.

To find the volume of the original rectangular prism, use the formula for volume: length × width × height. So for dimensions 5 cm (length), 6 cm (width), and 7 cm (height), the volume calculates to \(5 \times 6 \times 7 = 210 \mathrm{~cm}^{3}\). Now, since the prism is dilated by a scale factor of 4, the new volume becomes \(210 \times 4^3 = 210 \times 64 = 13,440 \mathrm{~cm}^{3}\) due to the fact that volume scales with the cube of the dilation factor! Want to impress your friends at your next dinner party? Try explaining how dilating shapes works! You could share that when you change the size of a 3D object, its volume changes by the cube of the scale factor. For example, if you have a prism with volume \(210 \mathrm{~cm}^{3}\) and you double its size, you’re actually multiplying the volume by \(2^3\) (which is 8), leading to a new volume of \(1680 \mathrm{~cm}^{3}\). It's one wild geometric world out there!