S2 - 7th Grade \( \begin{array}{l}\text { The difference between drizzle and rain has to do } \\ \text { with the size of the drops, not how much water is } \\ \text { actually falling from the sky. If rain consists of } \\ \text { drops larger than } 0.02 \text { in. in diameter, and drizzle } \\ \text { consists of drops less than } 0.02 \text { in. in diameter, } \\ \text { what can you say about the surface area of rain } \\ \text { and drizzle? }\end{array} \)

To understand the difference in surface area between rain and drizzle, we need to consider the relationship between the diameter of a drop and its surface area. 1. **Understanding Surface Area of a Sphere**: The surface area \( A \) of a sphere is given by the formula: \[ A = 4\pi r^2 \] where \( r \) is the radius of the sphere. The radius \( r \) is half of the diameter \( d \): \[ r = \frac{d}{2} \] 2. **Relating Diameter to Surface Area**: Substituting \( r \) in the surface area formula, we get: \[ A = 4\pi \left(\frac{d}{2}\right)^2 = \pi d^2 \] This shows that the surface area of a drop is proportional to the square of its diameter. 3. **Comparing Rain and Drizzle**: - For rain, the diameter \( d_r \) is greater than \( 0.02 \) in. - For drizzle, the diameter \( d_d \) is less than \( 0.02 \) in. 4. **Surface Area Calculation**: - The surface area of a rain drop can be expressed as: \[ A_r = \pi d_r^2 \] - The surface area of a drizzle drop can be expressed as: \[ A_d = \pi d_d^2 \] 5. **Conclusion**: Since \( d_r > 0.02 \) and \( d_d < 0.02 \), it follows that: \[ d_r^2 > (0.02)^2 \quad \text{and} \quad d_d^2 < (0.02)^2 \] Therefore, the surface area of rain drops \( A_r \) is greater than the surface area of drizzle drops \( A_d \): \[ A_r > A_d \] In summary, the surface area of rain drops is greater than the surface area of drizzle drops due to the larger diameter of rain drops compared to drizzle drops.