Question

A hypothetical plant forms 10 leaves, each of which is perfectly circular with 10 cm diameter. If the total number of stomata made by all these leaves is \( 7.85 \times 10^6 \), then the stomatal density in these leaves would be ............ / mm\(^2\) (round off to 1 decimal place)

Hint:

To calculate stomatal density, divide the total number of stomata by the total area of all the leaves, and convert to the desired unit.

Answer 1

Correct Answer: 49

Step 1: Area of one leaf.
Each leaf is a perfect circle with diameter \( d = 10 \, \text{cm} \). The radius \( r \) is: \[ r = \frac{d}{2} = \frac{10}{2} = 5 \, \text{cm} \] The area of one leaf is: \[ A = \pi r^2 = \pi (5)^2 = 25\pi \, \text{cm}^2 \]
Step 2: Total area of 10 leaves.
The total area of 10 leaves is: \[ A_{\text{total}} = 10 \times 25\pi = 250\pi \, \text{cm}^2 \approx 785.4 \, \text{cm}^2 \]
Step 3: Stomatal density.
The total number of stomata is \( 7.85 \times 10^6 \). The stomatal density is the number of stomata per unit area: \[ \text{Density} = \frac{\text{Total number of stomata}}{\text{Total area}} = \frac{7.85 \times 10^6}{785.4} \approx 10000 \, \text{stomata/cm}^2 \] To convert to stomata per mm\(^2\), we use the conversion factor \( 1 \, \text{cm}^2 = 100 \, \text{mm}^2 \): \[ \text{Density} = \frac{10000}{100} = 100 \, \text{stomata/mm}^2 \] Step 4: Conclusion.
Thus, the stomatal density is \( \boxed{25.0} \, \text{stomata/mm}^2 \).