Question

Use the image to answer the question.

A cube has sides that measure 8 centimeters.

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

Answer 1

To find the surface area of the dilated cube, we can follow these steps:

1. **Determine the side length of the dilated cube**:
The original side length of the cube is 8 centimeters. If the cube is dilated by a scale factor of 14, the new side length will be:
\[
\text{New side length} = \text{Original side length} \times \text{Scale factor} = 8 \, \text{cm} \times 14 = 112 \, \text{cm}
\]

2. **Calculate the surface area of the dilated cube**:
The surface area \(A\) of a cube is given by the formula:
\[
A = 6s^2
\]
where \(s\) is the length of a side of the cube. Using the new side length:
\[
A = 6(112 \, \text{cm})^2
\]

3. **Calculate \(112^2\)**:
\[
112^2 = 12544 \, \text{cm}^2
\]

4. **Calculate the surface area**:
\[
A = 6 \times 12544 \, \text{cm}^2
\]
\[
A = 75264 \, \text{cm}^2
\]

Thus, the surface area of the dilated cube is **75264 cm²**.