A solid cube has an edge length of 5. what is the ratio of the cube's surface area of its volume?

Answer

To solve the problem of finding the ratio of the surface area to the volume of a solid cube with an edge length of 5, we can follow these steps:

### Step 1: Calculate the Surface Area of the Cube
The formula for the surface area (SA) of a cube is given by:
\[ \text{SA} = 6 \times \text{side}^2 \]
Given that the edge length (side) of the cube is 5, we can substitute this value into the formula:
\[ \text{SA} = 6 \times 5^2 \]
Calculating \(5^2\):
\[ 5^2 = 25 \]
Now substituting back:
\[ \text{SA} = 6 \times 25 = 150 \]

### Step 2: Calculate the Volume of the Cube
The formula for the volume (V) of a cube is given by:
\[ \text{V} = \text{side}^3 \]
Again, substituting the edge length of 5:
\[ \text{V} = 5^3 \]
Calculating \(5^3\):
\[ 5^3 = 125 \]

### Step 3: Find the Ratio of Surface Area to Volume
Now that we have both the surface area and the volume, we can find the ratio:
\[ \text{Ratio} = \frac{\text{Surface Area}}{\text{Volume}} = \frac{150}{125} \]
To simplify this ratio, we can divide both the numerator and the denominator by 25:
\[ \frac{150 \div 25}{125 \div 25} = \frac{6}{5} \]

### Final Answer
The ratio of the cube's surface area to its volume is:
\[ \text{Ratio} = 6 : 5 \]

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