Question

If the cube 8cm 8cm 8cm is dilated by a scale factor of 1/4 what would be the surface area of the dilated cube?

Answer 1

To find the surface area of a cube after it has been dilated by a scale factor, we first need to calculate the original surface area of the cube and then apply the scale factor.

1. **Original dimensions of the cube**:
The sides of the cube are 8 cm each.

2. **Surface area of the original cube**:
The surface area \( A \) of a cube with side length \( s \) is given by the formula:
\[
A = 6s^2
\]
For our cube:
\[
A = 6 \times (8 \text{ cm})^2 = 6 \times 64 \text{ cm}^2 = 384 \text{ cm}^2
\]

3. **Dilated cube's side length**:
When the cube is dilated by a scale factor of \( \frac{1}{4} \):
\[
\text{New side length} = \frac{1}{4} \times 8 \text{ cm} = 2 \text{ cm}
\]

4. **Surface area of the dilated cube**:
Now, we find the surface area of the dilated cube with the new side length:
\[
A_{\text{new}} = 6 \times (2 \text{ cm})^2 = 6 \times 4 \text{ cm}^2 = 24 \text{ cm}^2
\]

Thus, the surface area of the dilated cube is \( \boxed{24} \) cm².