Question

Similar Figures and Volume Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 2 of 52 of 5 Items Question Use the image to answer the question. The two cubes are similar in shape. Compare the volume of the two and determine the scale factor from the smaller cube to the larger cube. Enter your response as a fraction. (1 point) Remaining Attempts : 3 Skip to navigation page 13 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the scale factor from the smaller cube to the larger cube and compare their volumes, you can follow these steps:

1. Identify the side lengths of the cubes: Let's say the side length of the smaller cube is \( s_1 \) and the side length of the larger cube is \( s_2 \).

2. Calculate the scale factor: The scale factor from the smaller cube to the larger cube is expressed as a fraction: \[ \text{Scale Factor} = \frac{s_2}{s_1} \]

3. Calculate the volumes of the cubes: The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] Therefore:

   • The volume of the smaller cube \( V_1 = s_1^3 \)
   • The volume of the larger cube \( V_2 = s_2^3 \)

4. Volume ratio: The ratio of the volumes of the two cubes is related to the cube of the scale factor: \[ \frac{V_2}{V_1} = \left( \frac{s_2}{s_1} \right)^3 \] Thus, you can express the volume comparison as: \[ \frac{V_2}{V_1} = \left(\text{Scale Factor}\right)^3 \]

If you provide the side lengths of the two cubes or if there is an image with the specifics, I would be able to assist you further in calculating the exact scale factor and volume comparison.