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Use the image to answer the question. A cube has sides that measure 8 centimeters. If the cube displayed is dilated by a scale...Question
Use 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 1/4
, what would be the surface area of the dilated cube?
(1 point)
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)
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Answered by
GPT-4o mini
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:
\[
\boxed{24 \text{ cm}^2}
\]
\[
\text{Surface Area} = 6s^2
\]
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:
\[
\boxed{24 \text{ cm}^2}
\]
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