the volume and surface area of a deer is 1,50, 000 `cm^(3) and 19, 000 cm^(2)`and of a squirrel is ` 625 cm ^(3) and 530 cm ^(3)` . The area available for heat loss per `cm^(3)` volume of the squirrel will be approximately

Options

A. Seven times more than the deer
B. Eleven times less than the deer
C. Three times more than the deer
D. Eleven times more than the deer

Answer

To solve the problem of determining the area available for heat loss per cm³ of volume for the squirrel compared to the deer, we can follow these steps:

### Step 1: Understand the Given Data
We have the following data:
- Deer:
- Volume = 150,000 cm³
- Surface Area = 19,000 cm²
- Squirrel:
- Volume = 625 cm³
- Surface Area = 530 cm²

### Step 2: Calculate the Surface Area to Volume Ratio
The surface area to volume ratio is calculated using the formula:
\[ \text{Surface Area to Volume Ratio} = \frac{\text{Surface Area}}{\text{Volume}} \]

#### For the Deer:
\[ \text{Ratio}_{\text{deer}} = \frac{19,000 \, \text{cm}^2}{150,000 \, \text{cm}^3} = \frac{19,000}{150,000} \approx 0.1267 \, \text{cm}^{-1} \]

#### For the Squirrel:
\[ \text{Ratio}_{\text{squirrel}} = \frac{530 \, \text{cm}^2}{625 \, \text{cm}^3} = \frac{530}{625} \approx 0.848 \, \text{cm}^{-1} \]

### Step 3: Compare the Ratios
Now, we will compare the surface area to volume ratios of the squirrel and the deer to find out how many times more the area available for heat loss per cm³ is for the squirrel compared to the deer.

#### Calculate the ratio of the two:
\[ \text{Comparison Ratio} = \frac{\text{Ratio}_{\text{squirrel}}}{\text{Ratio}_{\text{deer}}} = \frac{0.848}{0.1267} \approx 6.69 \]

### Step 4: Conclusion
The area available for heat loss per cm³ of volume of the squirrel is approximately 7 times more than that of the deer.

### Final Answer:
The area available for heat loss per cm³ volume of the squirrel will be approximately **7 times more than the deer**.

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