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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)

Answer 1

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

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

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

First, we calculate the surface area of the original cube:

1. The length of a side of the original cube is \( s = 8 \) cm.
2. Calculate the surface area of the original cube:

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

Next, we apply the dilation with a scale factor of \( \frac{1}{4} \):

1. The new side length of the dilated cube will be:

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

2. Now we calculate the surface area of the dilated cube:

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

Thus, the surface area of the dilated cube is:

\[ \boxed{24 \text{ cm}^2} \]