Question

se 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, you need to follow these steps:

1. **Calculate the original surface area of the cube**: The formula for the surface area \( A \) of a cube is given by:

\[
A = 6s^2
\]

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

For the original cube with \( s = 8 \) cm:

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

2. **Determine the new side length after dilation**: When a cube is dilated by a scale factor, the new side length \( s' \) can be calculated as:

\[
s' = \text{scale factor} \times s
\]

For a scale factor of 14:

\[
s' = 14 \times 8 = 112 \text{ cm}
\]

3. **Calculate the surface area of the dilated cube**: Now we use the new side length to calculate the surface area of the dilated cube:

\[
A' = 6(s')^2 = 6(112^2)
\]

First, calculate \( 112^2 \):

\[
112^2 = 12544
\]

Then calculate the surface area:

\[
A' = 6(12544) = 75264 \text{ cm}^2
\]

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