Question

Similar Figures and Surface Area Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 4 of 54 of 5 Items Question Use the image to answer the question. If the cube displayed is dilated by a scale factor of 14 , what would be the surface area of the dilated cube? (1 point) cm2 Remaining Attempts : 3 Skip to navigation page 16 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the surface area of the dilated cube, we first need to establish the surface area of the original cube and then apply the scale factor.

1. **Determine the original surface area of the cube:**
The surface area \( (SA) \) of a cube is given by the formula:
\[
SA = 6s^2
\]
where \( s \) is the side length of the cube.

2. **Apply the scale factor:**
If the cube is dilated by a scale factor of \( k \), the new side length will be:
\[
s' = k \cdot s
\]
The surface area of the dilated cube can be calculated using the new side length:
\[
SA' = 6(s')^2 = 6(k \cdot s)^2 = 6k^2s^2
\]
Therefore, the surface area of the dilated cube is \( k^2 \) times the surface area of the original cube.

3. **Calculate the surface area of the dilated cube:**
Given the scale factor \( k = 14 \), the new surface area will be:
\[
SA' = 6(14^2) \cdot s^2
\]
\[
SA' = 6 \cdot 196 \cdot s^2
\]
\[
SA' = 1176 \cdot s^2
\]

4. **Final Answer:**
The surface area of the dilated cube is \( 1176 \cdot s^2 \), where \( s^2 \) is the area based on the original cube's side length.

If you have the value for \( s^2 \), you can multiply that by 1176 to get the specific numerical surface area. Otherwise, the surface area of the dilated cube in terms of \( s \) is \( 1176s^2 \) cm².