Use the image to answer the question.

Question

A cube has sides that measure 8 centimeters.

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

(1 point)
cm2

Answer 1

To find the surface area of a cube, you can use the formula:

\[ \text{Surface Area} = 6s^2 \]

where \( s \) is the length of a side of the cube.

1. The original side length of the cube is \( 8 \) cm. First, we calculate the surface area of the original cube:

\[ \text{Surface Area} = 6(8^2) = 6 \times 64 = 384 \text{ cm}^2 \]

2. The cube is then dilated by a scale factor of \( \frac{1}{4} \). The new side length \( s' \) of the dilated cube is:

\[ s' = 8 \times \frac{1}{4} = 2 \text{ cm} \]

3. Now, we calculate the surface area of the dilated cube:

\[ \text{Surface Area of Dilated Cube} = 6(s')^2 = 6(2^2) = 6 \times 4 = 24 \text{ cm}^2 \]

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