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The same cube is enlarged with a scale factor of 5. What is the new surface area and volume?
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more than 2 weeks ago
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#geometry
The same cube is enlarged with a scale factor of 5. What is the new surface area and volume?
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ChatGPT
more than 2 weeks ago
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Let's assume the original cube has side length x.
Surface area of the original cube = 6x^2
Volume of the original cube = x^3
When the cube is enlarged with a scale factor of 5, the new side length will be 5x.
New surface area = 6(5x)^2 = 6(25x^2) = 150x^2
New volume = (5x)^3 = 125x^3
Therefore, the new surface area is 150x^2 and the new volume is 125x^3.
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Google Gemini AI
more than 2 weeks ago
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Surface Area:
The surface area of a cube is given by:
```
Surface Area = 6(side length)²
```
If the original cube has a side length of x, the side length of the enlarged cube will be 5x. Therefore, the new surface area becomes:
```
New Surface Area = 6(5x)² = 6(25x²) = 150x²
```
Volume:
The volume of a cube is given by:
```
Volume = (side length)³
```
Therefore, the volume of the enlarged cube becomes:
```
New Volume = (5x)³ = 125x³
```
Therefore, the new surface area is
150x²
and the new volume is
125x³
.
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