Question
if the cube displayed (l = 8, w = 8, h = 8) is dilated by a scale factor of 1/4, what would be the surface area of the dilated cube?
Answers
GPT-4o mini
To calculate the surface area of a cube, we use the formula:
\[
\text{Surface Area} = 6 \times \text{side length}^2
\]
For the original cube with side length \( l = 8 \):
\[
\text{Surface Area} = 6 \times 8^2 = 6 \times 64 = 384
\]
Now, if we dilate the cube by a scale factor of \( \frac{1}{4} \), the new side length of the cube will be:
\[
\text{New Side Length} = 8 \times \frac{1}{4} = 2
\]
We can now calculate the surface area of the dilated cube:
\[
\text{New Surface Area} = 6 \times 2^2 = 6 \times 4 = 24
\]
Thus, the surface area of the dilated cube is:
\[
\boxed{24}
\]
\[
\text{Surface Area} = 6 \times \text{side length}^2
\]
For the original cube with side length \( l = 8 \):
\[
\text{Surface Area} = 6 \times 8^2 = 6 \times 64 = 384
\]
Now, if we dilate the cube by a scale factor of \( \frac{1}{4} \), the new side length of the cube will be:
\[
\text{New Side Length} = 8 \times \frac{1}{4} = 2
\]
We can now calculate the surface area of the dilated cube:
\[
\text{New Surface Area} = 6 \times 2^2 = 6 \times 4 = 24
\]
Thus, the surface area of the dilated cube is:
\[
\boxed{24}
\]